Is it permissible to settle a portion of a deceased person's debt to repay an amount taken from them without their knowledge, and is it permissible to incur debt for that purpose with the intention of repaying it from the inheritance?

If the money was taken while the father was fulfilling his obligatory maintenance, then this is a sin that can be expiated by sincere repentance and returning the money, even indirectly, such as contributing to the payment of the father's debts. However, if it was taken due to the father's negligence in providing obligatory maintenance, and it was taken only to the extent of need without excess, then it does not need to be returned; this is based on the Prophet, peace and blessings be upon him, saying to Hind bint Utbah: "Take what suffices you and your child in a reasonable manner."