Is it permissible for a son to fulfill a vow on behalf of his mother?

The nature of the vow must be clarified to determine the answer. Vows are of different types: some must be fulfilled, some are permissible, and some are forbidden. If it is among what is forbidden, then it is not permissible for your mother to fulfill it, nor is it permissible for you to fulfill it on her behalf, such as a vow of disobedience. If it is among what is permissible, then she may fulfill it or pay an expiation for an oath (kaffarat yameen), and you may fulfill the expiation on her behalf or fulfill the part of the vow that accepts deputization. If it is among what must be fulfilled and she is able, then she must fulfill it; otherwise, she must pay an expiation for an oath if she is unable. It is permissible for her to appoint you to fulfill it on her behalf if it is something that accepts deputization, like charity, Hajj, and Umrah, with their conditions, or to pay the expiation for an oath on behalf of the vow she was unable to fulfill. However, fasting does not expiate on her behalf, as it is a bodily act of worship that does not accept deputization. This is if the mother is alive; but if she has passed away, then it is permissible to fulfill the vow on her behalf.