Is it permissible to count the cost of Hajj for someone else, along with adding a discount of half a month's salary as leave in exchange for travel?

The cost of Hajj for a proxy is calculated based on what is sufficient to perform the rituals according to the custom of the people in his country. This expense includes all travel obligations, such as salary deduction if the proxy is unpaid. The proxy must return any remaining money after Hajj to the one who deputized him if alive, or to his heirs if deceased, because the one performing Hajj on behalf of another does not own the money given to him. However, if the pilgrim is hired, the costs depend on his agreement with the deputizer, including compensation for the percentage deducted from his salary, knowing that performing Hajj for a wage is a matter of scholarly disagreement, with the preponderant opinion being its permissibility.