Is it obligatory to fulfill a vow dedicated to Sayyid al-Badawi, or is it permissible to distribute it as inheritance? And if it is obligatory, what are the best ways to spend it? And is this vow even valid to begin with?

If a father vows money to a deceased person, his vow is an act of polytheism (shirk) that is not valid and must not be fulfilled, by scholarly consensus, and one must repent from it. However, if he vows the money for the construction of a shrine, it is a vow of disobedience, and it is likewise not valid. The majority of scholars hold that no expiation (kaffarah) is required for it. This money may be utilized and divided as part of the inheritance, and it is not permissible to spend it for the aforementioned purpose. It is recommended to donate it as charity on behalf of the father for good causes.