The Sunnah states that it is permissible to do Hajj on behalf of another in two cases: 

1 – If that person is deceased 

The evidence for that is the report narrated by Muslim (1149), according to which a woman asked the Prophet (peace and blessings of Allaah be upon him) about her mother who had died, and she said: “O Messenger of Allaah, she never did Hajj; can I do Hajj on her behalf?” He said: “Yes, do Hajj on her behalf.” 

2 – If a person is unable to do Hajj himself because of something for which there is no hope that it will cease to affect him, such as an old man who cannot travel and put up with the hardships of Hajj, or a person who is chronically sick and there is no hope of recovery for him. 

The evidence for that is that a woman said: “O Messenger of Allaah, the obligation of Hajj has come when my father is an old man who cannot sit firmly on his mount. Can I perform Hajj on his behalf?” He said, “Yes.”  Narrated by al-Bukhaari (1513) and Muslim (1334). 

But if a person is unable to go for Hajj because he is banned from travelling outside his country, this is an impediment which it is hoped will be removed. Many of those who were banned from travelling outside their countries are able to do so after a while, either because of a change in government or for other reasons. 

It says in Fataawa al-Lajnah al-Daa’imah li’l-Ifta (11/51): 

It is permissible for the Muslim who has done the obligatory Hajj for himself to do Hajj on behalf of someone else, if the other person is unable to do Hajj for himself because he is old or sick with no hope of recovery, or because he is dead, because of the saheeh ahaadeeth which speak of that. But if the one on whose behalf he wants to do Hajj cannot do Hajj because of an impediment which it is hoped will be removed, such as a sickness from which there is hope of recovery, or political reasons, or because the route is not safe, and so on, then it is not permissible to do Hajj on his behalf. End quote. 

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

Based on this, it is not permissible for this person who is banned from travelling to appoint someone to perform Hajj on his behalf, rather he should wait until this impediment is lifted and he is able to do Hajj for himself.