The company continues to automate and enhance MoneyGram 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. MoneyGram offers an efficient, fast and secure way to send money around the world. MoneyGram Today the company MoneyGram International - an independent U.S. company, whose shares are traded on the New York Stock Exchange and MoneyGram money transfer is considered one of the largest international money transfer systems without opening a bank account.