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: high-speed delivery of transfers (10-15 min). Today the company MoneyGram International - an independent U.S. company, whose shares are traded on the New York Stock Exchange and MoneyGram money transfer is considered one of the largest international money transfer systems without opening a bank account. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.