After the correction of tariffs, volumes of MoneyGram transfers increased by 30%. AgentConnect continues to be an attractive alternative for businesses that choose to integrate their networks and point-of-sale platforms with the MoneyGram wired transfer. How quickly the money will reach the recipient? MoneyGram Money Order comes anywhere in the world in 10 minutes. Using the MoneyGram system, you can easily send money to your relatives and friends in other countries. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc.