The greatest increases in In due time MoneyGram separated from the Western Union and became an independent brand. The benefits of money transfers by MoneyGram: the payment of transfers is made in cash. MoneyGram launched a new in-person bill payment service which will be delivered through agents in their domestic network, giving consumers an easy, low-cost method to pay their bills. 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.