If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. Money transfers via MoneyGram system can be used as by bank customers, and by people who do not have bank accounts. The greatest increases in After the correction of tariffs, volumes of MoneyGram transfers increased by 30%. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. 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.