If you need to cancel or change a transaction, then you should contact by telephone with the MoneyGram branch agent, made the transaction for you. 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. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. The benefits of money transfers by MoneyGram: branching of network of the implementation of transfers across the world.