MoneyGram wired transfer implemented many changes to its technology platforms designed to prevent or detect suspicious transactions. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. 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. In whatever part of the world you are, you can trust your money transfer to the company MoneyGram.