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. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. Bank services of MoneyGram on money transfer are available only to individuals. The benefits of money transfers by MoneyGram: high-speed delivery of transfers (10-15 min).