How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. Bank services of MoneyGram on money transfer are available only to individuals. 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. MoneyGram point-of-sale systems are continually upgraded to provide the latest new products and functionality.