If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. Since going public two and a half years ago, MoneyGram has made great strides by pouring energy and resources into several critically important areas for business. 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.