by John Burnett:
You should get a certified copy of the executor's court appointment. I also suggest contacting the other bank to verify there is an account for the estate ready to receive the check from your bank. Make the check payable to the Estate.
There are no CIP requirements at your end.
by Brian Crow:
You are closing an account and creating a cashier's check. That does not make either the executor or the estate your customer for the purposes of CIP. You should follow whatever internal procedures you have for verifying the legitimacy of the request and that the executor has been appointed by the court (e.g. by obtaining letters of office/administration) prior to disbursing the funds.