Wired money transfer system MoneyGram is no longer new to us. According to statistics, every 4th person knows about it, or at least heard. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. What are the main benefits of money transfers by MoneyGram? Reliability - the international payment system gives complete assurance that the money will be paid to the recipient. The benefits of money transfers by MoneyGram: branching of network of the implementation of transfers across the world.