The company continues to automate and enhance MoneyGram 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. The benefits of money transfers by MoneyGram: high-speed delivery of transfers (10-15 min).