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: branching of network of the implementation of transfers across the world. In March 2012, the company MoneyGram merged with the network of U.S. payment centers ZipZap.