Very intensive and focused approach has helped MoneyGram to grow business at a rapid pace and establish MoneyGram as a global player in the marketplace. 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. It is very convenient and quick to transfer money without opening accounts and having no payment cards, precisely due to this wired transfer system MoneyGram has become one of the most common worldwide. Today, MoneyGram - is the second world leader by the growth of money transfers between individuals and the dynamics of international network services.