The benefits of money transfers by MoneyGram: there is no need to open a checking account when implementing the transfer. MoneyGram International, Inc. - The U.S. financial company engaged in operations in the international financial markets since 1940. 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.