Being free from guilt by returning the additional money to its owner

Q: I cashed a check from a bank in Makkah Al-Mukarramah. I received fifty bundles of Saudi fifty riyal banknotes, each bundle counted for five thousand riyals. I gave one of these bundles to a relative of mine to buy some things. When my relative was to pay the money to the seller, the latter discovered that the bundle contained one American banknote for one hundred dollar i.e. the value thereof is more than three hundred Saudi riyals. The seller changed it, got fifty riyals, and returned the rest. I enquired as to how could I get rid of this extra sum of money? Somebody told me that I should give it back to the bank but I was not satisfied with this because the sum of money concerned does not belong to the bank. Rather, it may belong to the Treasury or to one of the customers of the bank. Please tell me what is the proper way of getting rid of that money so that I am discharged of the responsibility towards it and that such money is given back to whom it is due. May Allah reward you with the best.

(Part No. 14; Page No. 76)  A: You have to return the extra money you got to the bank that gave it to you by mistake. If you do so, you will be discharged of all responsibility. It is impermissible for you to do any other thing with the extra money concerned. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.