Is it permissible to pay the cost of a lottery Hajj in Egypt on behalf of the wife's father, by a husband who will perform Hajj on his behalf, in exchange for the husband undertaking to commission someone to perform Hajj on behalf of his paternal grandfather or grandmother, and is it permissible for the husband to take this money provided that he donates whatever remains of it afterwards on behalf of the wife's father, and what is the ruling on this Hajj?

Your husband's performance of Hajj on behalf of your father is valid if he has already performed Hajj for himself and intended the Hajj for your father before entering the rituals. You are not obligated to pay him a fee unless you both agreed upon it beforehand, as he is performing it voluntarily. However, if you wish to reward him financially so that he may commission someone to perform Hajj on behalf of his grandfather or grandmother, that is good. Or, if you stipulated that any remaining money after the Hajj should be given as charity on behalf of your father, there is no harm in that, and he is obligated to fulfill this condition.