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. Thousands of businesses count on MoneyGram for payment services to move money and drive commerce. This is a trust that MoneyGram takes very seriously. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.