The greatest increases in The company installed more than 23,000 new MoneyGram signs around the globe, making it easier for consumers to find MoneyGram agents. Money orders and official checks by MoneyGram continue their steady performance and expanded line of bill payment services deliver excellent results. 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.