The benefits of money transfers by MoneyGram: there is no need to open a checking account when implementing the transfer. AgentConnect allows MoneyGram agents to integrate the money transfer service with their internal security and training processes. 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. Around the world, MoneyGram is working with leading financial institutions. 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.