In due time MoneyGram separated from the Western Union and became an independent brand. Since going public two and a half years ago, MoneyGram has made great strides by pouring energy and resources into several critically important areas for business. 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.