In due time MoneyGram separated from the Western Union and became an independent brand. Since going public two and a half years ago, MoneyGram has made great strides by pouring energy and resources into several critically important areas for business. 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.