The benefits of money transfers by MoneyGram: there is no need to open a checking account when implementing the transfer. To find MoneyGram agents will help you easily recognizable logo, as well as our website which will help you find the nearest location to send and receive money via MoneyGram. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. Today the company MoneyGram International - an independent U.S. company, whose shares are traded on the New York Stock Exchange and MoneyGram money transfer is considered one of the largest international money transfer systems without opening a bank account.