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(post deleted by author)

BUT, I can't for the life of me remember why.

All chargers charge and any battery can be used while charging, it just means it takes longer to charge. The reason for using a solar LiPo charger was very probably because you wanted to use a charger designed for use with a solar panel and a LiPo battery, which is a pretty good idea.

Different types of battories calls for different charging technic in order to achieve maximum life time and performance of the battory. It is so easy to fry or run down battories by charging them the wrong way. Battory and charger must be compatible.

Because the sun doesn't shine at night.

And a solar charger will magically make the sun shine?

No, but the battery that's included will keep the power going.

Oh and btw, does anyone know if you can mount a solar panel under a street lantern? Will it work? Is it illegal?

Legality will depend on your locality, but not likely any country has laws against placing a solar panel under a street lantern as such, but there may be laws against placing stuff in public space, or mounting stuff to a public street lantern.

Anyway, not likely that the dim light of a street lantern is going to have your solar panel produce any significant power.

Well, that's what I thought too. But I did some more googleing and found out you can't actually use a battery while it's charging with a normal charger.

iI think that's nonsense. All you need is a small amount of common sense, and use a charger that can deliver more than Arduino needs. How hard is that? If you have run the battery dead flat, it may hog the charger initially. You may have experienced that with a tablet or phone and could happen with Arduino.

Thus the charger won't be able to provide a full 4.2v, and thus will be unable to fully charge the battery.

If there is more power available at the solar cell than the Arduino is currently using, then the charger absolutely can bring the voltage up to the desired level. If there isn't enough power (night time or cloudy) then the Arduino uses the battery plus whatever is available from solar.

I use this charger (even though it's differently purposed) to charge a 250mAh LiPo for my "retirement clock" (a scrolling, text based countdown clock.) A small 5 volt solar panel sits in my south facing window, and the thing has run 24/7 for almost 2 years now without a problem.

Maybe you wanted a charger able to do maximum power point tracking?