Is it permissible for a debtor to buy gold from his female creditor at a price lower than the market price, and then pay off his debt to her with the gold he bought from her?

It is permissible to buy gold pounds from your sister with现款 (cash on hand), and then repay the loan from it, because these are two separate contracts. Immediate exchange (spot transaction) is a condition for selling gold for cash, because currencies are treated like gold and silver.

However, if the purpose of the purchase is to repay the loan, it is sufficient to calculate the price of gold on the day of repayment and repay the loan directly with cash. It is permissible to borrow in one currency and repay in another at the rate of the day of repayment, unless otherwise agreed upon at the beginning of the loan, based on the hadith: "There is no harm in taking it at its price on that day, as long as you do not separate and there is something between you." However, it is not permissible to stipulate this at the time of the loan contract, as it would constitute currency exchange without immediate exchange.