Changing a pick up is fairly easy first it unscrews, next unsolders and it's off they're just as easy to replace.
But before you refit the stator to the scooter check the fit of the pickup against the laminates the pickup should sit in line no part of it should protrude.
First pic showing the old pickup with a straight edge against the laminated core.

The second pic showing the new pickup again with a straight edge.
If you look closely you can see the new pickup protrudes further than the laminates of the stator. The pickup itself has two small laminated cores that protrude from the plastic of the pickup.

The ruler is slightly missing the top laminate of the stator which means the pickup is protruding, this could cause the flywheel to rub the pickup.
If the flywheel rubs it will cause the pickup to fail rapidly.
On this pickup the small top laminate is proud by about 0.7mm.
The easy fix is to file the pick up flush with the laminates of the stator, it will not harm the pickup or cause any other issues but it will stop the flywheel rubbing.
Mark.