How to send money via MoneyGram money transfer? To make up a money transfer you should go to the MoneyGram agents and fill the application form for transfer. MoneyGram's consumers and agents expect reliability and safety and that is precisely what MoneyGram continues to deliver, transaction by transaction. 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. In March 2012, the company MoneyGram merged with the network of U.S. payment centers ZipZap.