After getting more information and finding out this contract has already been completed I do not see how anything can be corrected. If the contract had never been awarded to this vendor and they had decided to start work without an award, then the Government would not owe the contractor anything. A vendor starting work before receiving an award is performing at their own risk. The vendor was fortunate in this case because they ended up receiving the award four days after they started performance.
From what you said, you do not know if there was a verbal award. You need to contact the former contracting officer and ask that specific question. If there was an early verbal award a memo for record should be added to the file stating you spoke to the former contracting officer and ____ is the date of the verbal award. Or you will find out there was no verbal award and if that is the case, you should also add a memo for record to the file stating there was not a verbal award.