The benefits of money transfers by MoneyGram: there is no need to open a checking account when implementing the transfer. Technology continues to play a key role in increasing MoneyGram transaction speed, automating and streamlining processes, and creating new functionality. 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. What are the main benefits of money transfers by MoneyGram? Individual flexible service. The recipient has the opportunity to receive money at any MoneyGram office anywhere in the world. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc.