solar battery charger

No--It will not...

Batteries can be very sensitive to charging conditions. You need to know what kind of battery (lead acid flooded cell/agm/gel/sealed or Li Ion of some type).

Voltage is the electrical equivalent of water pressure--Your charging voltage has to exceed the battery voltage to get current to move into the battery.

There are a few small charge controllers, such as from Genasun, that can take lower voltage from solar panels and step them up to higher voltages.

https://genasun.com/all-products/solar-charge-controllers/for-lithium/gvb-8a-li-lithium-solar-boost-controller/

Over charging batteries can result in a high risk of smoke/fire--And certain types of Li Ion are particularly vulnerable.

-Bill

There are a lot of differing Li Ion chemistries/construction out there--Need to know which one and charging details to be safe.

Regarding range boosting, it can be done--But do a little math first. Figure out how many Watt*Hours per mile you use--And how much a "reasonably sized" solar panel can supply. In general, a solar panel for a mobile operation does not add much range and can cause other issues (large panel picks up wind/causes drag/blow you over, glass panels are easy to shatter, etc.).

If you get (made up number) 1 mile per 100 WH, and you want to extend your range 5 miles, very roughly:

• 5 miles * 100 WH/mile * 1/0.77 solar panel+controller derating * 1/4 hours of sun per day (not-winter) = 162 Watt solar panel
• 45 watt panel * 0.77 panel+controller derating * 4 hours of sun per day = 139 Watt*Hours per day (full sun from 9am-3pm minimum)

In general, you are probably better of making  a "charging kiosk" where you park the scooter (work or home)--But the whole project is generally not worth the costs.

-Bill