Using the MoneyGram system, you can easily send money to your relatives and friends in other countries. What are the main benefits of money transfers by MoneyGram? Cost. Today, it is most advantageous to the customer service of all the similar services. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. MoneyGram company operates around the clock and all 7 days a week, so the time of money transfer takes only 10 minutes. MoneyGram financial results were driven by money transfer business, which delivered more than 40 percent growth in transaction volume.