If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. MoneyGram wired transfer implemented many changes to its technology platforms designed to prevent or detect suspicious transactions. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. AgentConnect continues to be an attractive alternative for businesses that choose to integrate their networks and point-of-sale platforms with the MoneyGram wired transfer. MoneyGram Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. The benefits of money transfers by MoneyGram: the opportunity to send a telegram with money transfer (up to 10 words) for free.