If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. International company MoneyGram has expanded its service capabilities of online money transfers to UK residents. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. Bank services of MoneyGram on money transfer are available only to individuals. MoneyGram launched a new in-person bill payment service which will be delivered through agents in their domestic network, giving consumers an easy, low-cost method to pay their bills.