Technology continues to play a key role in increasing MoneyGram transaction speed, automating and streamlining processes, and creating new functionality. At the heart of MoneyGram is trust and reliability of customers. You can quickly send and receive money, as money transfers usually come to the recipient within 10 minutes. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. The benefits of money transfers by MoneyGram: sender of of transfer can choose to receive a money transfer currency - U.S. dollars or euros.