The benefits of money transfers by MoneyGram: there is no need to open a checking account when implementing the transfer. 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. Using the MoneyGram system, you can easily send money to your relatives and friends in other countries. FormFreeSM phone-based offering allows businesses to reduce labor costs and create an excellent consumer experience by leveraging MoneyGram Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc.