Legal Question in Credit and Debt Law in Pennsylvania

NO, not directly. Your father's estate will be liable for his credit card debt. Being an authorized user does not make your mother personally liable for your father's credit card debt. Has she used the card at all? Perhaps an argument can be made that she needs to pay for the charges she made prior to or after his death.

This is such a small amount that if your father has some assets, his executor may be able to settle some of the debt. If there are no assets at all and no probate, then I would have your mother write to the creditors, tell them father has died (send copy of death certificate), tell them mother is not personally liable for the debts and that father has no probate assets justifying probate and that no estate will be set up. Ask them to close the account and not bother the mother. Send the letter certified mail and keep a copy.