Is it permissible for a father to mortgage his house to another person for a sum greater than the initial amount so that his son can benefit from the difference to prepare for his marriage, knowing that the first transaction involved usury?

Your father is not permitted to mortgage the house in the manner described, as it involves the lender benefiting from the house in exchange for the loan. This is prohibited and considered usury (riba). The lender must grant a respite to the debtor who is in hardship until he can afford the required amount, as Allah Almighty says: "And if there is one in hardship, then [let there be] a delay until [a time of] ease. But if you remit [it as] charity, it is better for you, if you only knew." The amount he is legally obligated to [return] is the difference between the loan amount and the market rental value for the lender's unlawful use of the house. It is permissible for the lender to hold the house as collateral without benefiting from it, unless it is for market rental value or more, to remove the suspicion of usury. Your father is not permitted to enter into this transaction again unless he fears imprisonment for non-payment; in that case, it is permissible out of necessity. It is not permissible to mortgage the house for a larger amount to take the difference under the pretext of marriage, because the need for marriage is not a necessity that permits usury.