How to send money via MoneyGram money transfer? To make up a money transfer you should go to the MoneyGram agents and fill the application form for transfer. 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. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. MoneyGram point-of-sale systems are continually upgraded to provide the latest new products and functionality. 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.