You should notify the local Social Security office to stop the payments. This does not happen automatically because the agency does not know your father passed away. I am sorry for your loss.
My condolences for your loss.
Often whoever legally handles disposition of the remains-- funeral parlor, crematory, etc.-- will notify Social Security. Be aware that Social Security benefits must be returned if the decedent did not live through the end of the month. This is commonly a problem for benefits directed deposited. It take Social Security some unexplained long time to reclaim the last month's benefits, so the direct deposit account should not be closed until that claim is made.
Best wishes for an outcome you can accept, and please remember to designate a best answer.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.
You or whoever has control of his checking account has to notify social security. They will pay the funeral amount, and will tell you how much to refund.