Praise be to Allah.
Allaah says in His Holy Book:
“. . . Hajj to the House [Ka‘bah] is a duty that mankind owes to Allaah, those who can afford the expenses (for one’s conveyance, provision and residence]; and whoever disbelieves, then Allaah stands not in need of any of the ‘Aalameen [mankind and jinn].” [Aal ‘Imraan 3:97]
The scholars’ discussion of the ability to perform Hajj revolves around the availability of a means of transport and sufficient money for the journey there and back, as well as sufficient funds to cover one’s family’s needs during one’s absence, freedom from debt, good health, security on the way, and - for women - a mahram (blood relative within the prohibited degrees of marriage, or a husband).
The issue of your Muslim friend revolves around the question of health, so we will focus on this matter here:
With regard to the interpretation of the aayah (verse of the Qur’aan) quoted above, ‘Ikrimah (may Allaah have mercy on him) said: “Sabeel [paraphrased in the phrase ‘those who can afford the expenses’] means health.” (Tafseer Ibn Katheer).
One of the conditions of Hajj being obligatory is that a person should be free of physical illness and disability that would prevent him from performing Hajj. If a person is suffering from a chronic illness, permanent disability, paralysis (that makes him unable to walk) or is very old and unable to move about, then there is no obligation to perform Hajj.
If a person is able to perform Hajj with the help of another, then it becomes a duty to perform Hajj when such help is available. (al-Mawsoo‘ah al-Fiqhiyyah, 17/34).
Ibn Katheer, may Allaah have mercy on him, said: “There may be different categories of ability. Sometimes a person may be able to perform Hajj by himself, and sometimes with the help of others, as is stated in the books of Ahkaam (Islamic rulings).” (Tafseer of the aayah previously quoted).
Whoever suffers from a permanent disability that prevents him from performing Hajj must appoint someone to perform Hajj on his behalf. If his disability is not permanent, then he should wait until he has recovered, then perform Hajj for himself; he is not permitted to appoint someone to perform Hajj on his behalf.
This is the answer to your question, which I hope you will convey to your friend. I do not want to miss this opportunity to thank you for your concern and interest in finding out the Islamic rulings in this situation which has to do with the fifth pillar of Islam. I also wish to encourage and invite you to join us in Islam. Peace be with you.