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. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. What are the main benefits of money transfers by MoneyGram? Reliability - the international payment system gives complete assurance that the money will be paid to the recipient. Keep in mind that if your locality there are several banks, working with MoneyGram and you will convert the currency received, before receiving check currency rates in several points - they can vary.