If the IRS determines that the original payment was lost, I believe they would send a replacement check. It would not be handled as a tax credit, and your mother would not amend her tax return. When she gets the results of the trace, it will tell her how to proceed.
Please note that the amount of the payment from Letter 6475 will not appear on her tax return. She must enter that amount in TurboTax, but the result on her tax return is that Form 1040 line 30 will be blank (or zero).
