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. The benefits of money transfers by MoneyGram: the payment of transfers is made in cash. 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.