There are conditions without which Hajj Badal might not be accepted:
The person appointed to perform Hajj Badal must be a sane Muslim.
While entering into Ihram, he should make intention on behalf of the person for whom he/she will perform Hajj Badal.
Hajj Badal must be performed by the appointed person only unless he has been authorized to get it done by another person. In this case, he/she can send some else in his/her place.
The appointed person who performs Hajj Badal should perform Hajj according to the desire of the person who sent him (Hajj Al-Tamattu, Hajj Al-Qiran).
He must put on Ihram only on behalf of the person who sent him and not for himself.
The person appointed for Hajj should not miss any imperative (Fard) part of it as no type of compensation renders Hajj Badal validly performed.
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Source: go-makkah.com