From Randy Carey:
"Our problem is that he doesn't have a Social Security Number."
I highly doubt that. He just does not want to give it to you.
Tell him to take the checks somewhere else.
31 U.S. Code § 5324 - Structuring transactions to evade reporting requirement prohibited
(a)Domestic Coin and Currency Transactions Involving Financial Institutions.—No person shall, for the purpose of evading the reporting requirements of section 5313(a) or 5325 or any regulation prescribed under any such section, the reporting or recordkeeping requirements imposed by any order issued under section 5326, or the recordkeeping requirements imposed by any regulation prescribed under section 21 of the Federal Deposit Insurance Act or section 123 of Public Law 91–508—
(2)cause or attempt to cause a domestic financial institution to file a report required under section 5313(a) or 5325 or any regulation prescribed under any such section, to file a report or to maintain a record required by any order issued under section 5326, or to maintain a record required pursuant to any regulation prescribed under section 5326, or to maintain a record required pursuant to any regulation prescribed under section 21 of the Federal Deposit Insurance Act or section 123 of Public Law 91–508, that contains a material omission or misstatement of fact;
From John Burnett:
The other issue here is whether you can cash those checks at all. You know the issuer is deceased. The funds in the account (assuming the grandmother was the sole owner and there was no POD designation) now belong to her estate. If it's been more than 10 days since her date of death, those checks are no longer properly payable since you have knowledge of the issuer's demise.