Performing Hajj on behalf of your father or mother is a kindness and beneficence to your parents. Allah will reward you greatly for doing so.Giving money to a woman to give to her husband in order to perform Hajj on behalf of your father is permissible as he is a proxy.
This is permissible if the proxy has previously performed Hajj for himself, and such is the case with the woman who will perform Hajj on behalf of your mother. It is permissible for a woman to perform Hajj on behalf of a man or a woman. There are authentic evidences reported from the Prophet (peace be upon him) in This regard. However, one who wishes to have another person perform Hajj on his behalf should (Part No. 11; Page No. 53) search for righteous and trustworthy persons in order to ensure that the rites of Hajj are performed properly.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.