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. Bank services of MoneyGram on money transfer are available only to individuals. MoneyGram 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. Today, MoneyGram - is the second world leader by the growth of money transfers between individuals and the dynamics of international network services.