Experienced consultants of MoneyGram will help you in execution of documents for payment and you will be pleasantly surprised by the speed of service. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year. MoneyGram financial results were driven by money transfer business, which delivered more than 40 percent growth in transaction volume.