John and June had a joint account with us. John received a pension direct deposit from MetLife and another direct deposit from Teachers Retirement Systems. June passed away so John removed her and added his son, Jim, to the account as an owner. A few months later, John passed away. Jim requested to hold off on removing John waiting for some kind of settlement. As time passed, it kind of fell through the cracks and has now fallen in my lap. We have removed John from the account, however both of his direct deposits are still coming in in his name. We feel that Jim is collecting on it knowing he shouldn't be receiving it because he has been very concerned about making sure nothing he does will stop the deposits from coming in. Our bookkeeping department said they aren't required and can't do anything with these like they would had it been a social security direct deposit. I am looking for any suggestions or input on how to handle this.

Despite what your bookkeeping department says, you need to stop accepting the deposits. They may not be subject to reclamation like Social Security deposits are, but they are still not your customer's funds

If Jim were to try to deposit a check payable to John, you would likely refuse the deposit. The same logic applies to John's ACH deposits. The bank has knowledge, and needs to act on that knowledge.

Your commentary about Jim suggests that he is maintaining this account solely for the purpose of receiving deposits that aren't his. For this reason, I would suggest exiting the relationship altogether.

Return the next received of those deposits using an R15 (you don't get extra time for returning them). Jim is apparently defrauding the two originators of those annuity payments. What says your bank won't be his next target? Terminate the relationship ASAP.