In due time MoneyGram separated from the Western Union and became an independent brand. The easiest way to send money via MoneyGram - is to use our website and find the nearest MoneyGram agent location. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. 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.