Is the fifty pounds I found at home, which my father reported missing, considered unlawful money if I take it to pay a debt to my mother, especially since my mother authorized me to do so, and my father is well-off?

It is not permissible for a son to take his father's money except with his permission, knowledge, and consent. An exception to this is if the father is stingy and does not provide the obligatory maintenance for his son, in which case it is permissible for the son to take from his money what is conventionally sufficient for him, without the father's knowledge. Therefore, if the father is not remiss in providing maintenance, it is not permissible to take the 50 pounds, and it must be returned. The father's wealth is not a justification for taking his money unjustly. However, if he does not provide the obligatory maintenance, it is permissible to take from his money conventionally.