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. The company continues to automate and enhance MoneyGram Very intensive and focused approach has helped MoneyGram to grow business at a rapid pace and establish MoneyGram as a global player in the marketplace. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. For the recipient MoneyGram service of wired transfer is free. All expenses will be paid by the sender at the time of sending money.