Previously existing BSA regulations define what is a "person:"
31CFR103.11(z) Person. An individual, a corporation, a partnership, a trust or estate...
The estate is the customer. It is the estate whose information you must obtain and whose identity you must verify. A copy of the court order appointing the personal representative (may or may not be an attorney) is your principal source of verification.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.