If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. International company MoneyGram has expanded its service capabilities of online money transfers to UK residents. 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. Using the MoneyGram system, you can easily send money to your relatives and friends in other countries.