The benefits of money transfers by MoneyGram: no fixup (the recipient may request payment at any MoneyGram agent in the country of receiving). Technology continues to play a key role in increasing MoneyGram transaction speed, automating and streamlining processes, and creating new functionality. 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.