If your room take up the whole game screen (a bit like your image), there not much you can do, because you do need to have part of that orange circle both on the left and on the right of the screen.
If your world is large and you platformer center its view on the character, there's more hope. Let's say your world has a width of
h. For example, split your world in two parts, at about the x-distance
h/2. Whenever the character is in the left part, leave the object overlapping the vertical side with coordinates at about
0. Whenever he is in the right part, add
h to their x-position.
Of course this creates a lot of computation if the character crosses the side a lot, so it's improvable. For example you could split down even further, and have the changes made only when the character crosses the
-h/4 to teleport him/her at
3*h/4 and when he/she crosses
5*h/4 to teleport him/her at