Reference: Majmoo’ Fataawa wa Rasaa.il ‘Abdul-‘Azeez ibn Baaz – Volume 16, Pages 402-403
Question: A man died without having performed the obligatory hajj, and instructed that hajj be performed on his behalf from his estate [upon his death]. [So] the question is about the correctness of [this] hajj, and whether the hajj on behalf of another is equal [in reward] to him having performed hajj on behalf of himself?
Response: If a Muslim dies and has not performed the obligatory hajj – while he has fulfilled all the conditions which render it obligatory upon him, then it is obligatory for hajj to be performed on his behalf from his estate which he has left; [this is the case] whether he has instructed for that to be done or not.
And if someone from amongst those who are qualified to do hajj performs hajj on his (i.e. Muhammad’s) behalf – and he has already performed the obligatory hajj on behalf of himself – then his hajj [on behalf of Muhammad] is correct, and will suffice him (Muhammad) in being relinquished of his obligation to perform hajj – just as he would if he (Muhammad) had done hajj on behalf of himself.
As for this being less or more [in reward], then that is [a matter] solely for Allaah (Subhaanahu wa Ta’aala) [alone]; that is because He [alone] Knows the affairs of his worshippers and their intentions. [Having said that], no doubt that which is obligatory is to hasten in fulfilling the obligation of the hajj if he is able [to do so] – before he dies. [This is] based upon the legislated evidences indicating that, and it is feared he will be liable for the sin of [unnecessarily] delaying [the hajj].