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 launched a new in-person bill payment service which will be delivered through agents in their domestic network, giving consumers an easy, low-cost method to pay their bills. 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. The benefits of money transfers by MoneyGram: the opportunity to send a telegram with money transfer (up to 10 words) for free.