MoneyGram wired transfer implemented many changes to its technology platforms designed to prevent or detect suspicious transactions. MoneyGram's consumers and agents expect reliability and safety and that is precisely what MoneyGram continues to deliver, transaction by transaction. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. The benefits of money transfers by MoneyGram: the opportunity to send a telegram with money transfer (up to 10 words) for free. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.