If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. 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. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. In whatever part of the world you are, you can trust your money transfer to the company MoneyGram.