What are the main benefits of money transfers by MoneyGram? Simple - the money transfer procedure is maximally simplified. In due time MoneyGram separated from the Western Union and became an independent brand. Millions of people around the world trust MoneyGram, as the wired transfer system provides its customers with a reliable, fast and inexpensive service. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc.