If I understand you correctly, the refund check that you did not cash was from the Department of Education, not from the IRS. It was a refund of an overpayment on your student loan, not a tax refund. Even though the overpayment on your student loan resulted from a mistaken offset of your income tax refund, the check from the Department of Education is not a tax refund. In that case, you cannot "claim" it or get credit for it on your tax return. Since it was not a tax refund from the IRS, you cannot use Form 3911. You have to ask the Department of Education how you can get a replacement for the check that they sent you.
