Unfortunately, I do not know of a way to move an established sketch from one component to another. The sketch is stuck with the active component during its creation.
One suggestion you may find is that you can copy and paste geometry from one active sketch into another. The steps to do this are:
1. Edit the sketch that contains the geometry you wish to move
2. Select all Sketch figures
3. Select Copy from the right click menu or use the keyboard shortcut for Copy command (Windows CTRL+C- Mac Command + C)
4. Stop Sketch
5. Activate the Component you wish to place the sketch in (select white circle next to the Component name in the browser to Activate Component)
6. Select the Work Plane or Face you wish to sketch on, Right mouse click and select Create Sketch
7. Select Paste from the right click menu or use the keyboard shortcut for Copy command (Windows CTRL+V- Mac Command + V) while in an active sketch.
8. Move Geometry as necessary (if necessary)
9. Stop Sketch
Note: New sketch will be created with identical sketch geometry. You may need to activate the top-level of the design to get back.
Please review this suggestion and let us know if it helps or if we may answer another question.
Thanks,
Nathan Chandler
Principal Specialist