@mbadx4 , it is possible and you would only transfer the game files. Those are the files under Applications. You must leave the Sims 4 folder (found Documents > Electronic Arts > Sims 4) on your Hard Drive otherwise you will not be able to save your game and the coding for the game always looks for that folder on your Hard Drive.
Playing the game off of an external hard drive will lead to slower response times from the game. To my knowledge step by step instructions on how to do this have never been written.
Please keep us updated.
