Is it permissible for a mother to pay off her son’s debt in exchange for him giving up an old air conditioner, knowing that the value of the debt is equivalent to the price of a new air conditioner, which has increased in price?

There is no objection to a mother paying off her daughter's debt in exchange for the daughter giving up the air conditioner. This is not usury (riba), because the money paid for the air conditioner is for a non-usurious commodity, and therefore it is permissible to sell the air conditioner at any price.