International company MoneyGram has expanded its service capabilities of online money transfers to UK residents. The company continues to automate and enhance MoneyGram 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. MoneyGram point-of-sale systems are continually upgraded to provide the latest new products and functionality.