What are the main benefits of money transfers by MoneyGram? Simple - the money transfer procedure is maximally simplified. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. MoneyGram hired compliance officers in many of their global offices to ensure compliance with regulations of specific countries or regions. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc.