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. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year. Today, MoneyGram - is the second world leader by the growth of money transfers between individuals and the dynamics of international network services.