Praise be to Allaah.
If a Muslim dies after he has become able to perform Hajj, then his heir has to do Hajj on his behalf himself, or he can delegate someone else to do Hajj for him, paid for from the money of the deceased, because this is a debt that he owes that is more deserving of being paid off. The delegate need not be one of the deceased person’s relatives. The sacrifice (qurbaan) which is done at the time of Hajj should be done in the name of the deceased father, not the name of the delegated person, if it is one of the requirements of Hajj. If the Hajj is “ifraad” (Hajj done on its own, without ‘Umrah), then there is no (obligatory) sacrifice, unless the delegated person does something prohibited for which the fidyah (compensatory sacrifice) is required.