move sketch from plane to plane.

RMC on the sketch in the FMT and select "Edit Sketch Plane" -> select new sketch plane.

First, make sure the plane you want to move your Sketch to was created before the Sketch existed.

If that is the case, right-click your Sketch in the FeatureManager and "Edit Sketch Plane"
Now select your other plane - either by selecting it in your tree or select it on screen.

Other things to ensure is that your plane is not hidden and that when going to View -> Planes that isn't turned off.