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 Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. It is very convenient and quick to transfer money without opening accounts and having no payment cards, precisely due to this wired transfer system MoneyGram has become one of the most common worldwide. The benefits of money transfers by MoneyGram: simplicity in making up.