What are the main benefits of money transfers by MoneyGram? Simple - the money transfer procedure is maximally simplified. 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. Around the world, MoneyGram is working with leading financial institutions. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940.