If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. Wired money transfer system MoneyGram is no longer new to us. According to statistics, every 4th person knows about it, or at least heard. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. The benefits of money transfers by MoneyGram: high level of data protection and confidentiality of money transfers. MoneyGram financial results were driven by money transfer business, which delivered more than 40 percent growth in transaction volume.