how to make a plain character look just like yours?

heres what i mean, just like in piggy, you see yourself in the cutscenes, but in other players screens, you also see yourself, so in one screen you see your character, and in the other you see you still see your character even though in the other screen it isnt, and both characters are at the same place, i have no idea how to make this, and i do not have a script, i tried everything, nothing worked, so if you can, please help (:

[i want the face, clothes, accessories, all to be the same, in your screen, the character looks just like you, in the other persons screen, it looks just like them!]