The benefits of money transfers by MoneyGram: there is no need to open a checking account when implementing the transfer. Very intensive and focused approach has helped MoneyGram to grow business at a rapid pace and establish MoneyGram as a global player in the marketplace. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. It is very convenient and quick to transfer money without opening accounts and having no payment cards, precisely due to this wired transfer system MoneyGram has become one of the most common worldwide. 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.