When sending the transfer via MoneyGram in one currency and receiving it in another, then currency conversion is carried out at the current rate of sales of current service point. 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.