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. In MoneyGram were added or converted new currencies in an additional 29 countries during the past year, providing consumers with a wide array of currency payout options. 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. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc.