The company installed more than 23,000 new MoneyGram signs around the globe, making it easier for consumers to find MoneyGram agents. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. MoneyGram offers an efficient, fast and secure way to send money around the world. 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.