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. The benefits of money transfers by MoneyGram: the payment of transfers is made in cash. Money orders and official checks by MoneyGram continue their steady performance and expanded line of bill payment services deliver excellent results. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.