If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. The greatest increases in How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. The benefits of money transfers by MoneyGram: high level of data protection and confidentiality of money transfers. What are the main benefits of money transfers by MoneyGram? Cost. Today, it is most advantageous to the customer service of all the similar services. MoneyGram company operates around the clock and all 7 days a week, so the time of money transfer takes only 10 minutes.