Very intensive and focused approach has helped MoneyGram to grow business at a rapid pace and establish MoneyGram as a global player in the marketplace. 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. 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.