If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. 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. Last year, MoneyGram business in the CIS and Eastern Europe took priority positions to increase the number of branches in comparison with other regions - were opened new four thousand branches.