First of all, it is important to know that Hajj is an obligatory duty on anyone who can do it physically and financially. So, if a person has the ability, no one else can do it on his behalf.
As Imam Ibn al-Mundhir states: “There is a virtual consensus among scholars that no one can do Hajj for another person who can perform it by himself.”
Therefore, a person can do hajj on behalf of another who is suffering from a terminal illness and hopes for no recovery, or an individual who is too old to travel, or someone who has passed away without having had the chance to do it.
Furthermore, ideally, according to all the scholars, a person who is performing Hajj on behalf of someone else must have performed Hajj on his behalf first.
The Prophet (peace and blessings be upon him) told someone who was intending to perform Hajj in the name of another relative that he should do so for himself first and then perform Hajj another time on behalf of the other person.
Almighty Allah knows best.
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