The greatest increases in The company continues to automate and enhance MoneyGram MoneyGram offers an efficient, fast and secure way to send money around the world. 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. Get information about the list of banks participating in the transfer system of MoneyGram, location and time of the closest points of service on the site of the system.