The benefits of money transfers by MoneyGram: there is no need to open a checking account when implementing the transfer. Wired money transfer system MoneyGram is no longer new to us. According to statistics, every 4th person knows about it, or at least heard. MoneyGram The Global Funds Transfer segment is the primary segment of MoneyGram, providing money transfer and bill payment services to consumers, who are often unbanked or underbanked. In March 2012, the company MoneyGram merged with the network of U.S. payment centers ZipZap.