An emphatic "no" unless he's with the current lessee, the widow. Your state law and/or the box lease should address who retains access to the box under a safe deposit box lease to two parties -- in most cases it will be the surviving lessee only.
If the Personal Representative cannot gain the cooperation of the surviving lessee, his only recourse is to get an order from the court. Presumably, his purpose is to review any property in the box and look for a will that might post-date any will that's already been discovered.
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John S. Burnett
BankersOnline.com
Fighting for Compliance since 1976
Bankers' Threads User #8