Please let me know if you can modify a contract after the period of performance ends to add funding to pay all invoices (or will I need to create a purchase order to make the payments). The required funds were available by not all provided on the contract. Thanks in advance for your assistance with this.
In a word – “Yes”!
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The fact the period of performance has expired is immaterial based on the scenario you provided. The reason is, not all of the contracting parties have completed their contractual requirements. In your case, the government hasn't paid the contractor the money they are owed for performance.
As a result, you would be unable to close out this contract and eventually the contractor could file a claim against the contract/government; see FAR 4.804-1 through 4.804-4 (it’s a short read).
What you will need to do is use funds that were (or still might be) available for new obligations during the FY the work was performed by the contractor in order to comply with fiscal law (time, purpose, amount). If the funds from that year are no longer available for new obligations your finance office will need to accomplish an OAR (obligation adjustment request) in order to certify those funds to be obligated with your contract modification.