Social Security benefits are not pro-rated. To be entitled to a Social Security benefit check for a given month, the person must be alive the entire month. No benefit is payable for the month of death.
This provision has been in the law since 1939 and can be changed only by an amendment to the Social Security Act. The legislative history of this provision does not show why benefits are not payable for the month of death. However, the provision complements the provision of the law that allows us to pay survivors benefits for the entire month of death.
You can return the check to your local Social Security office. If the payment is made by direct depost, the U.S. Treasury will automatically debit the bank account.