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EXHIBIT 2.40A

EXECUTION COPY

AMENDMENT TO SECURITIES PURCHASE AGREEMENT

This amendment (the “Amendment”) to that certain SECURITIES PURCHASE AGREEMENT, dated October 6, 2005 (the “Agreement”), is entered into on December 9, 2005 by and among Comverse, Inc., a Delaware corporation (“Purchaser”), CSG Software, Inc., a Delaware corporation (“CSG Software”), CSG Americas Holdings, Inc., a Delaware corporation (“CSG Holdings”), CSG Netherlands BV, a company organized under the laws of the Netherlands (“CSG Netherlands”) and CSG Technology Limited, a company organized under the laws of Bermuda (“CSG Technology” and, together with CSG Software, CSG Holdings and CSG Netherlands, the “Companies”), CSG Systems International, Inc., a Delaware corporation (“CSG”), and CSG Netherlands CV, a partnership with limited liability organized under the laws of The Netherlands (“CSG Netherlands CV” and, together with CSG, the “Sellers”), with CSG Netherlands CV acting through its general partner, CSG International Holdings, LLC, a Delaware limited liability company (“CSG International”). Capitalized terms used but not defined herein shall have the meaning ascribed to such term in the Agreement.

WHEREAS, Purchaser, the Sellers and the Companies are all parties to the Agreement;

WHEREAS, Purchaser, the Sellers and the Companies wish to amend the Agreement as provided herein; and

WHEREAS, pursuant to Section 11.4 of the Agreement, all amendments to or waivers of any provision of the Agreement may be made by a written instrument signed by the parties thereto.

NOW, THEREFORE, for good and valuable consideration, the receipt, adequacy and sufficiency of which are hereby acknowledged, the parties hereto, intending to be legally bound, covenant and agree as follows:

1. Amendments to the Agreement. The Agreement is hereby amended as follows:

(a) Section 1.1.

(i) The definition of “Cash Adjustment Amount” shall be deleted in its entirety and replaced with the following:

“Cash Adjustment Amount” means the sum of (a) the amount payable, if any, by Purchaser if Purchaser elects to acquire the Excess Cash Amount calculated in accordance with Section 7.3(e), and (b) an amount equal to the lesser of (i) 70% of Closing Cash in excess of $1,700,000 and (ii) $4,410,000.

(ii) The definition of “Escrow Amount” shall be deleted in its entirety and replaced with the following:

“Escrow Amount” means $2.0 million.

(b) Section 2.5(a). Section 2.5(a) shall be amended by (i) replacing the reference to “$1,100,000” therein with “$1,700,000” and (ii) replacing the reference to “opening of business” in clause (C) of the definition of “Closing Working Capital” with “close of business.”

(c) Section 2.5(b). The first sentence of Section 2.5(b) shall be deleted and replaced in its entirety with the following sentence:

“Within 60 days following the Closing Date, Purchaser shall deliver to the Sellers an unaudited combined statement of net assets of the Companies and Subsidiaries (exclusive of the assets and Liabilities of the FairPoint Business) as of the close of business on the Closing Date; provided, however, that no purchase accounting adjustments shall be made to the items thereon solely as a result of the consummation of the closing of the transactions contemplated by the Agreement and shall exclude the effect (including the Tax effect) of any act, event or transaction occurring after the Closing and not in the ordinary course of business of any Company or any Subsidiary (the “Closing Net Assets Statement”), a statement of Closing Working Capital derived from the Closing Net Assets Statement (the “Closing Working Capital Statement”) and a statement of the Closing Cash, the Excess Cash Amount and the resulting Cash Adjustment Amount, if any, derived from the Closing Net Assets Statement (the “Closing Cash Statement”).”

(d) Section 7.3(e). Section 7.3(e) shall be deleted in its entirety and replaced with the following:

“The Companies and Subsidiaries shall have an aggregate of no more than $8,000,000 of Cash on hand; provided, however, that the condition contained in this Section 7.3(e) shall have no force or effect unless the Sellers shall have used their reasonable best efforts to extract Cash from the Companies and Subsidiaries (including a willingness to incur normal withholding or similar Taxes in connection therewith) and, provided further, if the condition contained in this Section 7.3(e) shall not have previously been satisfied, Purchaser shall have the right and option (but not the obligation) to cause such condition to be satisfied by (i) at any time following the date hereof, agreeing in writing to pay to the Sellers, in accordance with Section 2.5(d), 100% of the excess of the Cash remaining in the Companies and Subsidiaries as of the Closing Date in excess of $8,000,000 (the “Excess Cash Amount”), (ii) after the date that is 60 days following the date hereof, agreeing in writing to pay to the Sellers, in accordance with Section 2.5(d), 90% of the Excess Cash Amount or (iii) after the date that is 100 days following the date hereof, agreeing in writing to pay to the Sellers, in accordance with Section 2.5(d), 75% of the Excess Cash Amount.”

3. This Amendment shall be deemed an agreement in writing by Purchaser to pay the amounts contemplated by Section 7.3(e), as amended herein, in accordance with Section 2.5(d) as additional Purchase Price.

4. All references in the Agreement to “this Agreement,” and to all other words referring to the Agreement (such as “herein,” “hereto,” “herewith” and “hereunder”), shall be deemed to mean and refer to the Agreement, as amended by this Amendment. This Amendment and the rights and obligations of the parties under this Amendment shall be governed by, and construed and interpreted in accordance with, and the parties hereto agree to submit to the exclusive jurisdiction, of the state of New York, in connection with any action, suit or proceeding based on or arising under this Amendment. This Amendment may be executed in one or more counterparts, all of which constitute one and the same instrument. Each provision of this Amendment will be considered severable and if for any reason any provision which is not essential to the effectuation of the basic purposes of this Amendment is determined by a court competent jurisdiction to be invalid or unenforceable and contrary to existing or future applicable law, such invalidity will not impair the operation of or affect those provisions of this Amendment which are valid. In that case, this Amendment will be construed so as to limit any term or

provision so as to make it enforceable or valid within the requirements of any applicable law, and in the event such term or provision cannot be limited, this Amendment will be construed to omit such invalid or unenforceable provisions. The Agreement, as amended by this Amendment and by that certain side letter between Comverse and CSG with respect to the allocation of the Purchase Price, sets forth the entire understanding of the parties thereto with respect to all matters contemplated thereby and hereby and supersedes all previous agreements and understandings among them concerning such matters. No statements or agreements, oral or written, made prior to or at the signing hereof, shall vary, waive or modify the written terms hereof.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be signed on the date and year first above written.