The benefits of money transfers by MoneyGram: there is no need to open a checking account when implementing the transfer. The greatest increases in Using the MoneyGram system, you can easily send money to your relatives and friends in other countries. MoneyGram hired compliance officers in many of their global offices to ensure compliance with regulations of specific countries or regions. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. MoneyGram point-of-sale systems are continually upgraded to provide the latest new products and functionality. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.