What is the ruling on a person refusing to take a sum of money when he discovered a day later that he had not received it in full during a previous currency exchange?

The exchange of currencies requires actual possession (قبض) at the contract مجلس العقد (session). If the two parties involved in the exchange separate before taking possession, the exchange is invalid. The contract is valid for what has been taken into possession and void for what has not, according to the opinion that allows the division of a transaction. If the error was unintentional, there is no sin upon either of you. It is preferable to cancel the entire transaction and initiate a new, valid exchange contract.