Should he do Hajj on behalf of a relative who cannot travel for Hajj?

Praise be to Allah.

It is permissible for the Muslim who has done the obligatory Hajj to do Hajj on behalf of someone else if that person is not able to do Hajj himself because he is old or sick with no hope of recovery or because he is deceased, because of the saheeh ahaadeeth which speak of that. But if he cannot do Hajj for a temporary reason that he hopes will pass, such as a sickness from which he hopes to recover or for political reasons or because the route is not safe, then it is not acceptable to do Hajj on his behalf. End quote. 

And Allaah is the Source of strength. May Allaah send blessings and peace upon our Prophet Muhammad and his family and companions. End quote. 

Standing Committee for Academic Research and Issuing Fatwas 

Shaykh ‘Abd al-‘Azeez ibn ‘Abd-Allaah ibn Baaz, Shaykh ‘Abd al-Razzaaq ‘Afeefi, Shaykh ‘Abd-Allaah ibn Qa’ood.