How to send money via MoneyGram money transfer? To make up a money transfer you should go to the MoneyGram agents and fill the application form for transfer. 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. FormFreeSM phone-based offering allows businesses to reduce labor costs and create an excellent consumer experience by leveraging MoneyGram Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. Today the company MoneyGram International - an independent U.S. company, whose shares are traded on the New York Stock Exchange and MoneyGram money transfer is considered one of the largest international money transfer systems without opening a bank account.