The benefits of money transfers by MoneyGram: no fixup (the recipient may request payment at any MoneyGram agent in the country of receiving). 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 completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.