Since going public two and a half years ago, MoneyGram has made great strides by pouring energy and resources into several critically important areas for business. If you need to cancel or change a transaction, then you should contact by telephone with the MoneyGram branch agent, made the transaction for you. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. MoneyGram point-of-sale systems are continually upgraded to provide the latest new products and functionality.