If South-East becomes North, North-East becomes West and so on, what will South become?

Let us look at the standard directions on a compass. The angle between North and South-East is $135^{\circ }$ in the counter-clockwise direction.
According to the question:

* South-East rotates by $135^{\circ }$ counter-clockwise to become North.
* North-East rotates by $135^{\circ }$ counter-clockwise to become West.

Applying the same $135^{\circ }$ counter-clockwise rotation to South:

* Rotating South ($180^{\circ }$) by $135^{\circ }$ counter-clockwise brings us to the original position of North-East ($45^{\circ }$).

Thus, South will become North-East.