If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. MoneyGram offers an efficient, fast and secure way to send money around the world. What are the main benefits of money transfers by MoneyGram? Reliability - the international payment system gives complete assurance that the money will be paid to the recipient. The benefits of money transfers by MoneyGram: branching of network of the implementation of transfers across the world.