In due time MoneyGram separated from the Western Union and became an independent brand. What are the main benefits of money transfers by MoneyGram? Individual flexible service. The recipient has the opportunity to receive money at any MoneyGram office anywhere in the world. 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 benefits of money transfers by MoneyGram: simplicity in making up. 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.