FAR 45.106 does not differentiate between existing contracts and new awards with regard to property transfers. Is this a moot point, i.e., existing contracts and new awards are handled the same way when property transfers are involved? If so, then just identifying the property in the new award and authorizing the transfer does not execute the transfer itself.
If I understand your question, Yes--The transfer needs an audit trail that shows instructions were followed; authorization isn't execution.
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The Contractor may use an 1149 as a cover sheet for the property list, to document the shipment in place FROM Initial Contract, TO New Contract, Authorization: Mod #, Ship In Place, and clearly cross-reference the property list by the number of line items, value, or any other adequate description. The recipient can sign and date the 1149, if that's in accordance with the method described in Contractor's procedures for the receiving process.
The new contract must also comply with the FAR to gain the list of property and then the same transfer document can support the transaction for both the losing and gaining contract property accounts. Please don't hesitate to ask for further guidance if this answer is not entirely satisfactory. Thank you.