Form of Letter Agreement among the Registrant and its officers and directors and Fortress Acquisition Sponsor III LLC

Exhibit 10.2

[●], 2021

Fortress Value Acquisition Corp. III

1345 Avenue of the Americas

46th Floor

New York, New York 10105

Re: Initial Public Offering

Ladies and Gentlemen:

This letter (this “Letter Agreement”) is being delivered to you in accordance with the Underwriting Agreement (the “Underwriting Agreement”) to be entered into by and between Fortress Value Acquisition Corp. III, a Delaware corporation (the “Company”), and Deutsche Bank Securities Inc. and BofA Securities, Inc., as representatives (the “Representatives”) of the several underwriters (collectively, the “Underwriters”), relating to an underwritten initial public offering (the “Public Offering”), of 23,000,000 of the Company’s units (including up to 3,000,000 units that may be purchased to cover over-allotments, if any) (the “Units”), each comprised of one share of the Company’s Class A common stock, par value $0.0001 per share (the “Common Stock”), and one-fifth of one redeemable warrant. Each whole warrant (each, a “Warrant”) entitles the holder thereof to purchase one share of Common Stock at a price of $11.50 per share, subject to adjustment. The Units shall be sold in the Public Offering pursuant to a registration statement on Form S-1 and prospectus (the “Prospectus”) filed by the Company with the Securities and Exchange Commission (the “Commission”) and the Company shall apply to have the Units listed on the New York Stock Exchange. Certain capitalized terms used herein are defined in paragraph 11 hereof.

In order to induce the Company and the Underwriters to enter into the Underwriting Agreement and to proceed with the Public Offering and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, Fortress Acquisition Sponsor III LLC, a Delaware limited liability company (the “Sponsor”), and each of the undersigned individuals, each of whom is a director or member of the Company’s board of directors and/or management team (each, an “Insider” and collectively, the “Insiders”), hereby agrees with the Company as follows:

1. The Sponsor and each Insider agrees with the Company that if the Company seeks stockholder approval of a proposed Business Combination, then in connection with such proposed Business Combination, it, he or she shall (i) vote any shares of Capital Stock owned by it, him or her in favor of any proposed Business Combination and (ii) not redeem any shares of Capital Stock owned by it, him or her in connection with such stockholder approval.

2. The Sponsor and each Insider hereby agrees with the Company that in the event that the Company fails to consummate a Business Combination within 24 months from the closing of the Public Offering, or such later period approved by the Company’s stockholders in accordance with the Company’s amended and restated certificate of incorporation, the Sponsor and each Insider shall take all reasonable steps to cause the Company to (i) cease all operations except for

the purpose of winding up, (ii) as promptly as reasonably possible but not more than 10 business days thereafter, subject to lawfully available funds therefor, redeem 100% of the Common Stock sold as part of the Units in the Public Offering (the “Offering Shares”), at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay its taxes (less up to $100,000 of interest to pay dissolution expenses), divided by the number of then outstanding Offering Shares, which redemption will completely extinguish all Public Stockholders’ rights as stockholders (including the right to receive further liquidation distributions, if any), and (iii) as promptly as reasonably possible following such redemption, subject to the approval of the Company’s remaining stockholders and the Company’s board of directors, dissolve and liquidate, subject in each case to the Company’s obligations under Delaware law to provide for claims of creditors and other requirements of other applicable law. The Sponsor and each Insider agrees to not propose any amendment (i) to the Company’s amended and restated certificate of incorporation that would affect the substance or timing of the Company’s obligation to allow redemption in connection with the Company’s initial Business Combination or to redeem 100% of the Offering Shares if the Company does not complete a Business Combination within 24 months from the closing of the Public Offering or (ii) with respect to any other provision of the Company’s amended and restated certificate of incorporation relating to stockholders’ rights or pre-initial Business Combination activity, unless the Company provides its Public Stockholders with the opportunity to redeem their shares of Common Stock upon approval of any such amendment at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay its taxes, divided by the number of then outstanding Offering Shares.

The Sponsor and each Insider acknowledges that it, he or she has no right, title, interest or claim of any kind in or to any monies held in the Trust Account or any other asset of the Company as a result of any liquidation of the Company with respect to the Founder Shares held by it, him or her. The Sponsor and each Insider hereby further waives, with respect to any shares of Common Stock held by it, him or her, if any, any redemption rights it, he or she may have in connection with the consummation of a Business Combination, including, without limitation, any such rights available in the context of a stockholder vote to approve such Business Combination or in the context of a tender offer made by the Company to purchase shares of Common Stock (although the Sponsor and the Insiders and their respective affiliates shall be entitled to redemption and liquidation rights with respect to any Offering Shares they hold if the Company fails to consummate a Business Combination within 24 months from the date of the closing of the Public Offering). The Sponsor and each Insider hereby further waives, with respect to any shares of Common Stock held by it, him or her, if any, any redemption rights it, he or she may have in connection with a stockholder vote to approve an amendment to the Company’s amended and restated certificate of incorporation (A) to modify the substance or timing of the Company’s obligation to allow redemption in connection with the Company’s initial Business Combination or to redeem 100% of the Offering Shares if the Company does not complete a Business Combination within 24 months from the closing of the Public Offering or (B) with respect to any other provision relating to stockholders’ rights or pre-Business Combination activity.

3. Notwithstanding the provisions set forth in 7(a) and (b) below, during the period commencing on the effective date of the Underwriting Agreement and ending 180 days after

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such date, the Sponsor and each Insider shall not, without the prior written consent of the Representatives, (i) sell, offer to sell, contract or agree to sell, hypothecate, pledge, grant any option to purchase or otherwise dispose of or agree to dispose of, directly or indirectly, or establish or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”) and the rules and regulations of the Commission promulgated thereunder, with respect to any Units, shares of Common Stock, Founder Shares, Warrants or any securities convertible into, or exercisable, or exchangeable for, shares of Common Stock owned by it, him or her, (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any Units, shares of Common Stock, Founder Shares, Warrants or any securities convertible into, or exercisable, or exchangeable for, shares of Common Stock owned by it, him or her, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (iii) publicly announce any intention to effect any transaction, including the filing of a registration statement, specified in clause (i) or (ii). The provisions of this paragraph will not apply (i) to the transfer of Founder Shares to any independent director appointed or elected to the Company’s board of directors after the Public Offering or (ii) if the release or waiver is effected solely to permit a transfer not for consideration and, in each case the transferee has agreed in writing to be bound by the same terms described in this Letter Agreement to the extent and for the duration that such terms remain in effect at the time of the transfer. In addition, the provisions of this paragraph will not in any way limit the ability of the Sponsor to enter into agreements with employees of the Sponsor or any of its affiliates or employees of Fortress Investment Group LLC or any of its affiliates relating to the transfer of direct or indirect interests in the Founder Shares to such persons, provided that such transfer is not effected until the expiration of the Founder Shares Lock-Up Period (as defined below), or admitting such persons as members of the Sponsor, as long as, to the extent any reporting obligation under Section 16 of the Exchange Act is triggered as a result of such agreements, any related filing under Section 16 of the Exchange Act includes a practical explanation as to the nature of such agreement.

4. In the event of the liquidation of the Trust Account, the Sponsor (which for purposes of clarification shall not extend to any other shareholders, members or managers of the Sponsor) agrees to indemnify and hold harmless the Company against any and all loss, liability, claim, damage and expense whatsoever (including, but not limited to, any and all legal or other expenses reasonably incurred in investigating, preparing or defending against any litigation, whether pending or threatened, or any claim whatsoever) to which the Company may become subject as a result of any claim by (i) any third party for services rendered (other than the Company’s independent public accountants) or products sold to the Company or (ii) a prospective target business with which the Company has discussed entering into a transaction agreement (a “Target”); provided, however, that such indemnification of the Company by the Sponsor shall apply only to the extent necessary to ensure that such claims by a third party for services rendered (other than the Company’s independent public accountants) or products sold to the Company or a Target do not reduce the amount of funds in the Trust Account to below (i) $10.00 per Offering Share or (ii) such lesser amount per Offering Share held in the Trust Account due to reductions in the value of the trust assets as of the date of the liquidation of the Trust Account, in each case, net of the amount of interest earned on the property in the Trust Account which may be withdrawn to pay its taxes, except as to any claims by a third party (including a Target) who executed a waiver of any and all rights to seek access to the Trust

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Account and except as to any claims under the Company’s indemnity of the Underwriters against certain liabilities, including liabilities under the Securities Act of 1933, as amended. In the event that any such executed waiver is deemed to be unenforceable against such third party, the Sponsor shall not be responsible to the extent of any liability for such third party claims. The Sponsor shall have the right to defend against any such claim with counsel of its choice reasonably satisfactory to the Company if, within 15 days following written receipt of notice of the claim to the Sponsor, the Sponsor notifies the Company in writing that it shall undertake such defense. For the avoidance of doubt, none of the Company’s officers or directors will indemnify the Company for claims by third parties, including, without limitation, claims by vendors and prospective target businesses.

5. To the extent that the Underwriters do not exercise their over-allotment option to purchase up to an additional 3,000,000 Units within 45 days from the date of the Prospectus (and as further described in the Prospectus), the Sponsor agrees to forfeit, at no cost, a number of Founder Shares in the aggregate equal to 750,000 multiplied by a fraction, (i) the numerator of which is 3,000,000 minus the number of Units purchased by the Underwriters upon the exercise of their over-allotment option, and (ii) the denominator of which is 3,000,000. The forfeiture will be adjusted to the extent that the over-allotment option is not exercised in full by the Underwriters so that the number of Founder Shares will equal an aggregate of 20.0% of the Company’s issued and outstanding Capital Stock after the Public Offering. To the extent that the size of the Public Offering is increased or decreased, the Company will effect a stock dividend, share contribution back to capital or other appropriate mechanism, as applicable, with respect to the Founder Shares immediately prior to the consummation of the Public Offering in such amount as to maintain the number of Founder Shares prior to the Public Offering at 20% of the Company’s issued and outstanding Capital Stock of the Public Offering. In connection with such increase or decrease in the size of the Public Offering, then (A) the references to 3,000,000 in the numerator and denominator of the formula in the first sentence of this paragraph shall be changed to a number equal to 15% of the number of shares included in the Units issued in the Public Offering and (B) the reference to 750,000 in the formula set forth in the immediately preceding sentence shall be adjusted to such number of Founder Shares that the Sponsor would have to return to the Company in order for the number of Founder Shares to equal an aggregate of 20.0% of the Company’s issued and outstanding Capital Stock after the Public Offering.

6. The Sponsor and each Insider hereby agrees and acknowledges that: (i) the Underwriters and the Company would be irreparably injured in the event of a breach by such Sponsor or Insider of its, his or her obligations under paragraphs 1, 2, 3, 4, 5, 7(a), 7(b), and 9 of this Letter Agreement (ii) monetary damages may not be an adequate remedy for such breach and (iii) the non-breaching party shall be entitled to injunctive relief, in addition to any other remedy that such party may have in law or in equity, in the event of such breach.

7. (a) The Sponsor and each Insider agrees that it, he or she shall not Transfer any Founder Shares (or shares of Common Stock issuable upon conversion thereof) until the earliest to occur of: (A) one year after the completion of the Company’s initial Business Combination; (B) subsequent to the Company’s initial Business Combination, if the last reported sale price of the shares of Common Stock equals or exceeds $12.00 per share (as adjusted for stock splits, stock dividends, reorganizations, recapitalizations and the like) for any 20 trading days with any 30-trading day period commencing at least 150 days after the Company’s initial Business

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Combination; and (C) the date following the completion of the Company’s initial Business Combination on which the Company completes a liquidation, merger, stock exchange, reorganization or other similar transaction that results in all of the Company’s Public Stockholders having the right to exchange their share of common stock for cash, securities or other property (the “Founder Shares Lock-up Period”).

(b) The Sponsor and each Insider agrees that it, he or she shall not Transfer any Private Placement Warrants (or shares of Common Stock issued or issuable upon the conversion of the Private Placement Warrants), until 30 days after the completion of the Company’s initial Business Combination (the “Private Placement Warrants Lock-up Period”, together with the Founder Shares Lock-up Period, the “Lock-up Periods”).

(c) Notwithstanding the provisions set forth in paragraphs 7(a) and (b), Transfers of the Founder Shares, Private Placement Warrants and shares of Common Stock issued or issuable upon the exercise or conversion of the Private Placement Warrants or the Founder Shares and that are held by the Sponsor, Insider or any of their permitted transferees (that have complied with this paragraph 7(c)), are permitted (a) to the Company’s officers, directors or employees, any affiliates or family members of any of the Company’s officers, directors or employees, any members or employees of the Sponsor, or any affiliates of the Sponsor; (b) in the case of an individual, by gift to a member of the individual’s immediate family or to a trust, the beneficiary of which is a member of the individual’s immediate family or an affiliate of such person, or to a charitable organization; (c) in the case of an individual, by virtue of laws of descent and distribution upon death of the individual; (d) in the case of an individual, pursuant to a qualified domestic relations order; (e) by private sales or transfers made in connection with the consummation of a Business Combination at prices no greater than the price at which the securities were originally purchased; (f) in the event of the Company’s liquidation prior to the completion of an initial Business Combination; (g) by virtue of the laws of the State of Delaware or the Sponsor’s limited liability company agreement upon dissolution of the Sponsor; and (h) in the event of the Company’s liquidation, merger, capital stock exchange, reorganization or other similar transaction which results in all of the Company’s stockholders having the right to exchange their shares of Common Stock for cash, securities or other property subsequent to the completion of the Company’s initial Business Combination; provided, however, that in the case of clauses (a) through (e), these permitted transferees must enter into a written agreement agreeing to be bound by the restrictions herein.

8. The Sponsor and each Insider represents and warrants that it, he or she has never been suspended or expelled from membership in any securities or commodities exchange or association or had a securities or commodities license or registration denied, suspended or revoked. Each Insider’s biographical information furnished to the Company (including any such information included in the Prospectus) is true and accurate in all respects and does not omit any material information with respect to such Insider’s background. The Sponsor’s and each Insider’s questionnaire furnished to the Company is true and accurate in all respects. The Sponsor and each Insider represents and warrants that: it, he or she is not subject to or a respondent in any legal action for, any injunction, cease-and-desist order or order or stipulation to desist or refrain from any act or practice relating to the offering of securities in any jurisdiction; it, he or she has never been convicted of, or pleaded guilty to, any crime (i) involving fraud, (ii) relating to any financial transaction or handling of funds of another person, or (iii) pertaining to any dealings in any securities and it, he or she is not currently a defendant in any such criminal proceeding.

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9. Except as disclosed in the Prospectus, neither the Sponsor not any Insider nor any affiliate of the Sponsor or any Insider, shall receive from the Company any finder’s fee, reimbursement, consulting fee, monies in respect of any repayment of a loan or other compensation prior to, or in connection with any services rendered in order to effectuate the consummation of the Company’s initial Business Combination (regardless of the type of transaction that it is), other than the following, none of which will be made from the proceeds held in the Trust Account prior to the completion of the Company’s initial Business Combination: repayment of a loan and advances of up to an aggregate of $300,000 made to the Company by the Sponsor to cover offering-related and organizational expenses; payment to an affiliate of the Sponsor for office space, administrative and support services for a total of $20,000 per month; reimbursement for any out-of-pocket expenses related to identifying, investigating and consummating an initial Business Combination; and repayment of loans, if any, and on such terms as to be determined by the Company from time to time, made by the Sponsor or any of the Company’s officers or directors to finance transaction costs in connection with an intended initial Business Combination, provided, that, if the Company does not consummate an initial Business Combination, a portion of the working capital held outside the Trust Account may be used by the Company to repay such loaned amounts so long as no proceeds from the Trust Account are used for such repayment. Up to $1,500,000 of such loans may be convertible into warrants of the post Business Combination entity at a price of $1.50 per warrant at the option of the lender. Such warrants would be identical to the Private Placement Warrants.

10. The Sponsor and each Insider has full right and power, without violating any agreement to which it, he or she is bound (including, without limitation, any non-competition or non-solicitation agreement with any employer or former employer), to enter into this Letter Agreement and, as applicable, to serve as a director on the board of directors of the Company and hereby consents to being named in the Prospectus as a director of the Company.

11. As used herein, (i) “Business Combination” shall mean a merger, capital stock exchange, asset acquisition, stock purchase, reorganization or similar business combination, involving the Company and one or more businesses; (ii) “Capital Stock” shall mean, collectively, the Common Stock and the Founder Shares; (iii) “Founder Shares” shall mean the 5,750,000 shares of the Company’s Class F common stock, par value $0.0001 per share (up to 750,000 of which are subject to forfeiture depending on the extent to which the over-allotment option is not exercised by the Underwriters); (iv) “Private Placement Warrants” shall mean the Warrants to purchase up to 4,666,667 shares of Common Stock of the Company (or 5,066,667 shares of Common Stock if the over-allotment option is exercised in full) that the Sponsor has agreed to purchase for an aggregate purchase price of $7,000,000 in the aggregate (or $7,600,000 if the over-allotment option is exercised in full), or $1.50 per Warrant, in a private placement that shall occur simultaneously with the consummation of the Public Offering; (v) “Public Stockholders” shall mean the holders of securities issued in the Public Offering; (vi) “Trust Account” shall mean the trust fund into which a portion of the net proceeds of the Public Offering shall be deposited; and (vii) “Transfer” shall mean the (a) sale of, offer to sell, contract or agreement to sell, hypothecate, pledge, grant of any option to purchase or otherwise dispose of or agreement to dispose of, directly or indirectly, or establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call equivalent position within the

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meaning of Section 16 of the Securities Exchange Act of 1934, as amended, and the rules and regulations of the Commission promulgated thereunder with respect to, any security, (b) entry into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any security, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (c) public announcement of any intention to effect any transaction specified in clause (a) or (b).

12. This Letter Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby. This Letter Agreement may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument executed by all parties hereto.

13. No party hereto may assign either this Letter Agreement or any of its rights, interests, or obligations hereunder without the prior written consent of the other party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee. This Letter Agreement shall be binding on the Sponsor and each Insider and their respective successors, heirs and assigns and permitted transferees.

14. This Letter Agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York, without giving effect to conflicts of law principles that would result in the application of the substantive laws of another jurisdiction. The parties hereto (i) all agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this Letter Agreement shall be brought and enforced in the courts of New York City, in the State of New York, and irrevocably submit to such jurisdiction and venue, which jurisdiction and venue shall be exclusive and (ii) waive any objection to such exclusive jurisdiction and venue or that such courts represent an inconvenient forum.

15. Any notice, consent or request to be given in connection with any of the terms or provisions of this Letter Agreement shall be in writing and shall be sent by express mail or similar private courier service, by certified mail (return receipt requested), by hand delivery or facsimile transmission.

16. This Letter Agreement shall terminate on the earlier of (i) the expiration of the Lock-up Periods and (ii) the liquidation of the Company; provided, however, that this Letter Agreement shall earlier terminate in the event that the Public Offering is not consummated and closed by [•], 2021; provided further that paragraph 4 of this Letter Agreement shall survive such liquidation.

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Acknowledged and Agreed:

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