Wired money transfer system MoneyGram is no longer new to us. According to statistics, every 4th person knows about it, or at least heard. What are the main benefits of money transfers by MoneyGram? Cost. Today, it is most advantageous to the customer service of all the similar services. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year. In March 2012, the company MoneyGram merged with the network of U.S. payment centers ZipZap.