Is it forbidden to borrow a sum of money and return it in gold, and if so, does the borrower bear the sin for that if the lender insists on the agreement, and is it permissible for the sister to repay the debt without her husband's knowledge?

It is forbidden to agree, when concluding a loan contract, to repay it with its value in gold, due to the usury of nasi'ah involved, and because it is a deferred exchange (sarf). Therefore, it is not permissible to record a debt incurred in a specific currency as equivalent to the value of that currency in gold or another currency, with the debtor being obligated to repay it in gold or the other agreed-upon currency. If the borrower insists on this, it is permissible to give him the extra amount as a voluntary donation to prevent estrangement, not as a matter of entitlement. Similarly, it is permissible for the sister to voluntarily pay this amount to avoid problems and disputes.