hold the yoyo in front of you facing the catch zone with each half in one hand.
assuming the axle is free moving and neither side has a greater resistance to twisting, do the following to shift the axle:
hold the right half still, untwist the left half by a small angle. this will result in the left half alone being unscrewed without moving the axle from the right half.
then hold the left half still in its new position and twist the right half back. this again will rotate only the right half but not the axle.
after the yoyo is screwed back again, this results in an overall shift of the axle to the right side.