Hehe yeah thats the oldscool way like Super Mario World did the Player vs Player mini Battle. Its a simple Solution but it has no Transition and relies on a well defined known Screensize. Also the Character Width and Height takes a significant role in the Calculation because that decides if you get a Teleport effect or have to walk Completly out of the Screen before reapearing on the other screen.
But hey its a Solution after all =) if that is what he needs.