Money transfers via MoneyGram system can be used as by bank customers, and by people who do not have bank accounts. If you need to cancel or change a transaction, then you should contact by telephone with the MoneyGram branch agent, made the transaction for you. The company continues to automate and enhance MoneyGram MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. Millions of families depend on MoneyGram to safely send money home or pay the bills.