How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. MoneyGram launched a new in-person bill payment service which will be delivered through agents in their domestic network, giving consumers an easy, low-cost method to pay their bills. The benefits of money transfers by MoneyGram: high level of data protection and confidentiality of money transfers. The benefits of money transfers by MoneyGram: simplicity in making up. In March 2012, the company MoneyGram merged with the network of U.S. payment centers ZipZap.