If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. Since going public two and a half years ago, MoneyGram has made great strides by pouring energy and resources into several critically important areas for business. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. It is very convenient and quick to transfer money without opening accounts and having no payment cards, precisely due to this wired transfer system MoneyGram has become one of the most common worldwide. The benefits of money transfers by MoneyGram: simplicity in making up.