If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. Very intensive and focused approach has helped MoneyGram to grow business at a rapid pace and establish MoneyGram as a global player in the marketplace. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. In whatever part of the world you are, you can trust your money transfer to the company MoneyGram. Millions of families depend on MoneyGram to safely send money home or pay the bills.