Is it permissible for a friend to perform Hajj on behalf of the deceased, and how should the intention for that be made?

It is permissible for a Muslim who has performed the obligatory Hajj for himself to perform Hajj on behalf of another person who is unable to do so due to old age, an incurable illness, or death. There is no difference in this regard between parents and others, due to the saying of the Prophet, peace and blessings be upon him: "Perform Hajj for yourself, then perform Hajj for Shubrumah." Therefore, it is permissible for a man to perform Hajj on behalf of your brother if he has already performed the obligatory Hajj for himself.