The company continues to automate and enhance MoneyGram MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. What are the main benefits of money transfers by MoneyGram? Reliability - the international payment system gives complete assurance that the money will be paid to the recipient. 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.