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. At the heart of MoneyGram is trust and reliability of customers. You can quickly send and receive money, as money transfers usually come to the recipient within 10 minutes. The benefits of money transfers by MoneyGram: the opportunity to send a telegram with money transfer (up to 10 words) for free. The benefits of money transfers by MoneyGram: simplicity in making up.