THIRD SUPPLEMENTAL INDENTURE

Exhibit 4.ii(b)

THIRD SUPPLEMENTAL INDENTURE

This Third Supplemental Indenture (this “Supplemental Indenture”), dated as of October 19, 2004, is by and among Phosphate Resource Partners Limited Partnership (formerly known as Freeport-McMoRan Resource Partners, Limited Partnership), a Delaware limited partnership (the “Issuer”), Phosphate Acquisition Partners L.P., a Delaware limited partnership (“PAP”), and JPMorgan Chase Bank (formerly known as Chemical Bank), a New York banking corporation, as trustee under the Indenture referred to below (the “Trustee”).

W I T N E S S E T H:

WHEREAS, the Issuer has heretofore executed and delivered to the Trustee a Senior Indenture dated as of February 1, 1996 (as supplemented by a First Supplemental Indenture, dated as of February 14, 1996, and a Second Supplemental Indenture, dated as of December 23, 1996, the “Indenture”) providing for the issuance of unsecured debentures, notes or other evidences of indebtedness of the Issuer in series;

WHEREAS, pursuant to the Indenture, the Issuer has heretofore issued $150,000,000 aggregate principal amount of 7% Senior Notes due 2008 (the “Senior Notes”), all of which are outstanding as of the date hereof;

WHEREAS, pursuant to the Agreement and Plan of Merger, dated as of March 17, 2004, among IMC Global Inc., a Delaware corporation, PRP-GP LLC, a Delaware limited liability company and the Administrative Managing General Partner of the Issuer and PAP, FMRP Inc., a Delaware corporation and the Special General Partner of the Issuer and PAP, PAP and the Issuer (the “Merger Agreement”), the Issuer will be merged with and into PAP (the “Merger”), with PAP as the surviving entity in the Merger; and

WHEREAS, pursuant to Sections 8.1 and 9.1 of the Indenture, the Trustee is authorized to execute and deliver this Supplemental Indenture and the Issuer is permitted to effect the Merger upon execution and delivery of this Supplemental Indenture to the Trustee.

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the Issuer and PAP do hereby certify and agree as follows:

1. PAP is a limited partnership formed under the laws of the State of Delaware.

2. Upon consummation of the Merger, PAP, as the Successor Company within the meaning of Section 9.1 of the Indenture, shall assume the Issuer’s obligations to pay principal of (and premium or make whole amount, if any) and interest on all of the Senior Notes and the due and punctual performance and observance of all of the covenants and conditions contained in the Indenture.

3. PAP hereby agrees to provide the Trustee with prompt notice of the consummation of the Merger. In the event that the Merger Agreement is terminated and/or the Merger does not occur, then this Supplemental Indenture shall be null and void and have no force and effect.

4. For purposes of Section 11.4 of the Indenture, the address of PAP, as the Successor Company, is:

100 South Saunders Road

Lake Forest, Illinois 60045

Attention: Secretary

5. All Senior Notes authenticated and delivered after receipt by the Trustee of the notice referred to in Section 3 hereof shall bear the following notation, which may be stamped or imprinted thereon:

“In connection with the merger of Phosphate Resource Partners Limited Partnership (formerly known as Freeport-McMoRan Resource Partners, Limited Partnership) (the “Issuer”) into Phosphate Acquisition Partners L.P. (“PAP”) and pursuant to the Third Supplemental Indenture dated as of October 19, 2004, PAP has assumed the Issuer’s obligations to pay the principal of (and premium or make whole amount, if any) and interest on this Senior Note and the due and punctual performance and observance of all of the covenants and conditions contained in the Indenture.”

PAP shall arrange for and pay all expenses related to such notation.

6. This Supplemental Indenture is a supplemental indenture within the meaning of Section 8.1 of the Indenture, and the Indenture shall be read together with this Supplemental Indenture and shall have the same effect over the Senior Notes, in the same manner as if the provisions of the Indenture and this Supplemental Indenture were contained in the same instrument. In all other respects, the Indenture is confirmed by the parties hereto as supplemented by the terms of this Supplemental Indenture. Subject to Section 7 of this Supplemental Indenture, in the event that there is a conflict or inconsistency between the Indenture and this Supplemental Indenture, the provisions of this Supplemental Indenture shall control.

7. If any provision of this Supplemental Indenture limits, qualifies or conflicts with another provision which is required to be included in this Supplemental Indenture by the Trust Indenture Act of 1939, the required provision shall control. If any provision of this Supplemental Indenture modifies any Trust Indenture Act of 1939 provision that may be so modified, such Trust Indenture Act of 1939 provision shall be deemed to apply to this Supplemental Indenture as so modified. If any provision of this Supplemental Indenture excludes any Trust Indenture Act of 1939 provision that may be so excluded, such Trust Indenture Act of 1939 provision shall be excluded from this Supplemental Indenture.

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8. THIS SUPPLEMENTAL INDENTURE SHALL BE DEEMED TO BE A CONTRACT UNDER THE LAWS OF THE STATE OF NEW YORK, AND FOR ALL PURPOSES SHALL BE CONSTRUED IN ACCORDANCE WITH THE LAWS OF SUCH STATE, EXCEPT AS MAY OTHERWISE BE REQUIRED BY MANDATORY PROVISIONS OF LAW.

9. The parties may sign any number of copies of this Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement.

10. All agreements of the Issuer and PAP in this Supplemental Indenture shall bind their respective successors. All agreements of the Trustee in this Supplemental Indenture shall bind its successors.

11. In case any provision in this Supplemental Indenture shall be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

12. The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this Supplemental Indenture or for or in respect of the recitals contained herein, all of which recitals are made solely by the Issuer and by PAP.

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IN WITNESS WHEREOF, the parties hereto have caused this Third Supplemental Indenture to be duly executed as of the date first above written.