All perfect praise be to Allah. Blessings and peace be upon Prophet Mohammad and upon his family and companions.
There are two situations in which it is permissible to authorize someone to perform Hajj ( Major pilgrimage ) on behalf of another:
First: If Hajj was due on a Muslim, but he died before performing it, his heirs should authorize someone to perform Hajj on his behalf and cover all the Hajj expenses from the deceased's estate. It is also permissible for a Muslim, an heir of the deceased or not, to perform Hajj on his behalf voluntarily .
Second: If a Muslim was inflicted with an incurable disease, or was too old to travel, and was financially capable to cover the expenses of Hajj, then he should authorize someone to perform it on his behalf, even with paying him a wage. And Allah Knows Best.