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 International, one of the leading companies in the global money transfer market, has announced that its customers in Israel can now send and receive money transfers in Euro. The benefits of money transfers by MoneyGram: simplicity in making up. The benefits of money transfers by MoneyGram: branching of network of the implementation of transfers across the world.