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. Money orders and official checks by MoneyGram continue their steady performance and expanded line of bill payment services deliver excellent results. The benefits of money transfers by MoneyGram: the opportunity to send a telegram with money transfer (up to 10 words) for free.