Is it permissible for the husband's mother to perform Umrah on behalf of her deceased ex-husband if he had willed her to do so before his death?

There is no objection to a woman performing 'Umrah (definition) on behalf of her divorced husband, provided that she has already performed 'Umrah for herself. Ibn Hazm clarified the permissibility of a woman performing Hajj on behalf of a man or a woman, and a man performing Hajj on behalf of a woman or a man. He based his reasoning on prophetic traditions that permit this, and on the verse: "And do good" (Qur'an 22:77), considering this act to be among the permissible good deeds.