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. How to send money via MoneyGram money transfer? To make up a money transfer you should go to the MoneyGram agents and fill the application form for transfer. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. 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. The benefits of money transfers by MoneyGram: the transfer is available in the system to obtain within 90 days.