Praise be to Allah.
It is not permissible to do Hajj or ‘Umrah on behalf of anyone who is able to do them himself.
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said:
“With regard to appointing others to do Hajj or ‘Umrah on their behalf, this is something that, unfortunately, people at present have taken to extremes, that may be invalid according to Islam.
That is because there are two reports from Imam Ahmad as to whether it is permissible to appoint someone else to perform a nafl duty on one's behalf.
One report says that it is not permissible for a person to appoint someone else to do a nafl duty such as Hajj or ‘Umrah on his behalf, whether he is sick or healthy. This report seems to be more correct, because acts of worship should be done by a person himself, so that he may attain whatever worship and humility before Allah he can attain.
You can see the difference between a man who does Hajj for himself and a man who gives money to someone else to perform Hajj on his behalf. The latter does not gain the benefits of worship such as reforming his heart and humbling himself before Allah.
It is more like a financial transaction whereby he appoints someone else to buy and sell on his behalf.
If he is sick and wants to delegate someone to do a nafl deed on his behalf, we say that this is not something that is taught in the Sunnah. Rather the Sunnah is to appoint someone to do things on one's behalf with regard to fard (obligatory) actions only. The difference between fard and nafl is that the fard deed is binding upon a person, and if he cannot do it then he may appoint someone to do Hajj and ‘Umrah on his behalf. But nafl deeds are not obligatory, so it is said: So long as you are sick and you have done the obligatory action, then give praise to Allah for that, and spend the money that you wanted to give to someone to do Hajj or ‘Umrah on your behalf in other ways; use it to help a poor man who has not done the obligatory Hajj yet. That is better for you than saying, “Take this and do Hajj on my behalf,” even if you are sick.
As for the obligatory Hajj, people are not negligent about it, praise be to Allah. You can hardly find anyone who appoints someone else to do the obligatory Hajj on his behalf unless he is unable to do it.
This is something that is mentioned in the Sunnah, as in the hadith of Ibn ‘Abbas (may Allah be pleased with him), according to which a woman came to the Prophet (peace and blessings of Allah be upon him) and said: “O Messenger of Allah, the command of Allah to His slaves to perform Hajj has come when my father is an old man who cannot sit firmly in the saddle. Can I perform Hajj on his behalf?” He said: “Yes.”
Conclusion: There are two reports from Imam Ahmad about appointing someone else to perform a nafl duty on one's behalf. One of them says that it is not valid, and the other says that it is valid whether one is able or not.
But in my view it is undoubtedly more correct to say that it is not valid to appoint someone to do a nafl deed on one's behalf, whether one is able to do it or not. With regard to obligatory Hajj, the Sunnah says that the one who is unable to do it and has no hope that the situation will change may send someone on his behalf.” (Fatawa Ibn ‘Uthaymin, 21/140)
It says in Fatawa al-Lajnah al-Daimah (11/68):
“The Muslim who is able to perform Hajj should hasten to do it and in this case it is not permissible for him to appoint someone else to do Hajj on his behalf, and the Hajj of someone else will not suffice for him so long as he is able to perform Hajj himself.”
“The scholars of the Standing Committee favoured the view that one may perform Hajj and ‘Umrah on behalf of a living person who is unable to do them, even if it is nafl.”
It says in Fatawa al-Lajnah al-Daimah, 11/81
“If you have done ‘Umrah on your own behalf, it is permissible for you to do ‘Umrah on behalf of your mother and father if they are unable to do it because of old age or sickness for which there is no hope of recovery.”
This was also the view favoured by Shaykh Ibn Baz (may Allah have mercy on him), who was asked: I want to perform Hajj on behalf of my mother. Is it essential to ask her permission, knowing that she has already performed the obligatory Hajj?
“If your mother is unable to perform Hajj because of old age or sickness from which there is no hope of recovery, there is nothing wrong with your performing Hajj on her behalf, even if that is without her permission. It is proven that a man asked the Prophet (peace and blessings of Allah be upon him) for permission saying: O Messenger of Allah, my father is an old man who cannot do Hajj or ‘Umrah. The Messenger of Allah (peace and blessings of Allah be upon him) said: “Do Hajj and ‘Umrah on behalf of your father.”
And a woman asked him for permission, saying: “O Messenger of Allah, my father is an old man and he cannot perform Hajj or travel. Shall I perform Hajj on his behalf?” The Prophet (peace and blessings of Allah be upon him) said: “Do Hajj on behalf of your father.” Hajj may also be performed on behalf of the deceased, because of the sahih hadiths that have been narrated to that effect, and because of these two hadiths.” (Fatawa Ibn Baz, 16/414)
To conclude, it is not permissible to do Hajj or ‘Umrah on behalf of any living person who is able to do that, but in the case of one who is not able, if it is the obligatory Hajj then it is permissible, but if it is nafl then it is the subject of a difference of scholarly opinion.
And Allah knows best.