The company continues to automate and enhance MoneyGram 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 Global Funds Transfer segment is the primary segment of MoneyGram, providing money transfer and bill payment services to consumers, who are often unbanked or underbanked.