After the correction of tariffs, volumes of MoneyGram transfers increased by 30%. If you need to cancel or change a transaction, then you should contact by telephone with the MoneyGram branch agent, made the transaction for you. At the heart of MoneyGram is trust and reliability of customers. You can quickly send and receive money, as money transfers usually come to the recipient within 10 minutes. What are the main benefits of money transfers by MoneyGram? Cost. Today, it is most advantageous to the customer service of all the similar services. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc.