What should I do about a debt I want to repay, even though its owner swore not to take it back, and is it permissible for me to give the money in charity on his behalf?

If your friend swore not to take money and then took it, an expiation for breaking an oath (kaffarat yamin) is incumbent upon him. If your friend considered the money charity, he is not permitted to retract it and take the money. If you seek his permission to give the money as charity on his behalf, that would be considered a retraction on his part. You can reward your friend with a gift or an honorarium on another occasion, and it is not stipulated that it be of the same value as the money. You are not permitted to seek his permission to give charity on his behalf with this money, lest you cause him to fall into the forbidden act of retracting charity. However, you can give a general charity from your own money on his behalf, without being his agent or seeking his permission, and he will receive the reward for both charities.