In due time MoneyGram separated from the Western Union and became an independent brand. 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. The benefits of money transfers by MoneyGram: high-speed delivery of transfers (10-15 min).