I suggest you direct the manager of that post office to look at Postal Operations Manual section 612 "Delivery of Addressee's Mail to Another" and specifically at 612.11, which says that mail can be delivered to a competent member of an addressee's family - the only requirement is that "designation of another person to receive mail should be in writing, but no special form is required."
So assuming that the power of attorney form states clearly that your mother has the right to receive your father's mail, the postmaster is out of line.
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Follow Ms. Brewers advice. A Durable Power of Attorney does not have to be filed with the court. One of the reasons for having one is to avoid having to involve the court.
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I agree with the other respondents. A power of attorney is almost never "filed" with any court, and unless it has to do with real property it is not recorded with the County Recorder. In California, a petition can be filed under Probate Code Section 4941 to compel a third party to accept an agent's authority. While the US Government is probably immune from damages, others can be liable for attorneys' fees if they unreasonably refuse to accept the power of attorney, although such actions are rare.