How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. What are the main benefits of money transfers by MoneyGram? Cost. Today, it is most advantageous to the customer service of all the similar services. MoneyGram hired compliance officers in many of their global offices to ensure compliance with regulations of specific countries or regions. 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. The Global Funds Transfer segment is the primary segment of MoneyGram, providing money transfer and bill payment services to consumers, who are often unbanked or underbanked.