Since going public two and a half years ago, MoneyGram has made great strides by pouring energy and resources into several critically important areas for business. 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. MoneyGram 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.