In due time MoneyGram separated from the Western Union and became an independent brand. How to send money via MoneyGram money transfer? To make up a money transfer you should go to the MoneyGram agents and fill the application form for transfer. 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. The benefits of money transfers by MoneyGram: high-speed delivery of transfers (10-15 min). The benefits of money transfers by MoneyGram: simplicity in making up. MoneyGram company operates around the clock and all 7 days a week, so the time of money transfer takes only 10 minutes.