In due time MoneyGram separated from the Western Union and became an independent brand. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. 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. The benefits of money transfers by MoneyGram: the opportunity to send a telegram with money transfer (up to 10 words) for free.