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. The benefits of money transfers by MoneyGram: simplicity in making up. In whatever part of the world you are, you can trust your money transfer to the company MoneyGram. MoneyGram financial results were driven by money transfer business, which delivered more than 40 percent growth in transaction volume.