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. MoneyGram Thousands of businesses count on MoneyGram for payment services to move money and drive commerce. This is a trust that MoneyGram takes very seriously. In March 2012, the company MoneyGram merged with the network of U.S. payment centers ZipZap.