Reference: Majmoo’ Fataawa wa Rasaa.il ‘Abdul-‘Azeez ibn Baaz – Volume 16, Pages 403-404
Question: Is it permissible to perform ‘umrah on behalf of someone who has died? And is it permissible for me to perform ‘umrah on behalf of my father who is still alive, but is unable to do so [himself]?
Response: It is permissible to perform ‘umrah and hajj on behalf of the deceased if he was a Muslim, and like this it is permissible to perform ‘umrah and hajj on behalf of a Muslim who is alive if he is unable to do so himself due to old age or an illness that is not anticipated to pass. [And this is the case] whether it is your father, or your mother, or other than them. [This is] based upon what has been authentically reported from the Prophet ﷺ that a man asked him:
“O Messenger of Allaah, my father is very old, he cannot perform hajj [himself], nor can he ride on a mount; should I perform hajj on his behalf and ‘umrah [too]?” So the Prophet ﷺ said to him:
«Perform hajj on behalf of your father, and ‘umrah [too].» – transmitted by Imaam Ahmad no.15751 and an-Nasaa.ee no.2621.
And it has [also] been authentically reported from him ﷺ that a woman from Khath’am asked him, saying:
“O Messenger of Allaah, my father is very old, and he cannot sit firm on the mount, so should I perform hajj on his behalf?” He ﷺ said:
«Perform hajj on behalf of your father.» – transmitted by Imaam Ahmad no.3041 and an-Nasaa.ee no.2634.