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. FormFreeSM phone-based offering allows businesses to reduce labor costs and create an excellent consumer experience by leveraging 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. MoneyGram company operates around the clock and all 7 days a week, so the time of money transfer takes only 10 minutes.