What are the main benefits of money transfers by MoneyGram? Individual flexible service. The recipient has the opportunity to receive money at any MoneyGram office anywhere in the world. 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. MoneyGram Today the company MoneyGram International - an independent U.S. company, whose shares are traded on the New York Stock Exchange and MoneyGram money transfer is considered one of the largest international money transfer systems without opening a bank account.