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 - is an urgent money transfer by means of wired transfer around the world without opening a bank account. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. 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.