If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. MoneyGram - is an urgent money transfer by means of wired transfer around the world without opening a bank account. MoneyGram offers an efficient, fast and secure way to send money around the world. The benefits of money transfers by MoneyGram: the opportunity to send a telegram with money transfer (up to 10 words) for free. The benefits of money transfers by MoneyGram: simplicity in making up. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.