The greatest increases in 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. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. What are the main benefits of money transfers by MoneyGram? Reliability - the international payment system gives complete assurance that the money will be paid to the recipient. The benefits of money transfers by MoneyGram: the opportunity to send a telegram with money transfer (up to 10 words) for free.