The greatest increases in Very intensive and focused approach has helped MoneyGram to grow business at a rapid pace and establish MoneyGram as a global player in the marketplace. 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? Cost. Today, it is most advantageous to the customer service of all the similar services. Thousands of businesses count on MoneyGram for payment services to move money and drive commerce. This is a trust that MoneyGram takes very seriously.