Letters of Administration do expire. There should be an expiration date on it. You can get a new one from the Surrogates Court that issued it but the administrator can not delegate her duties by giving you a power of attorney because she is acting for a third party as administrator. You should hire an attorney to have a new Administrator of the estate appointed (you) due to the incapacity of the current Administrator.
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I agree with Attorney Chertock. What is the reason why your father's estate has been kept open for all this time? There is generally no reason for an estate to stay open for 35 years. Knowing the answer to that question might help suggest your next course of action.
You are not going to be able to sign for your mother regarding her duties as administrator.
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