You can check the stator winding that charges the battery just like the windings for the ignition. It should read .6 Ohms. Almost a short so you have to have a meter that reads low Ohms. I haven't seen many battery windings go bad. Usually it's the regulator/rectifier.
Here's what the original stator looks like on the motor with the flywheel removed. The red thing. It's a sealed unit. It has two sets of coils. One set is used to create voltage for the ignition system, the other set is used for charging the battery. The magnets on the underside of the flywheel just barely clear the outer circumference of the stator.
The CDI replacement below looks a little different, and the resistance readings are a little different but it does the same thing.