You’re welcome. Correct you cannot connect Powercore to be recharging it at the same time as take output from it. That is called pass-thru and doesn’t work on the Powercore 20100.
The 15W Anker panel should charge your iphone at close to full speed in strong sunshine, that is why it is so consistently highly reviewed and a good answer in sunny areas, wait for strong sunshine then try it. If it does then do this in sequence:
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when you see strong sunshine, plug in your iphone til its at 85% charged. Note: iphones respond badly to variable sunshine you might have to unplug phone and replug if you have variable sun (e.g. passing cloud). So for example if you are not geeky if you did it different like be in shade, plug solar-lightning-iphone then go into sun, the iphone will lock itself to a low recharge speed from being plugged in during shade and ignore the then later sunshine, so do exactly what I say, get into strong sunshine then plug in iphone, and no standing in front of the solar panel as you plug in as you will cause shade and the iphone won’t respond well to then the output going up after you walk away.
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once your iphone 85% charged, if you have strong sunshine, then charge your Powercore (*).
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if you encounter mains power then use Powerport2 to recharge your iphone and Powercore.
(*) I don’t know if the Powercore 20100 and Anker Powerport Solar Lite 15W are compatible, in that the 15W panel may not output high enough voltage to be above what the Powercore needs. Also if you use bad cables then the cable can be losing a lot power so the Powercore gets insufficient to trigger it to charge. Longer cables are more likely bad than shorter cables as there is more length for a fault to appear and longer cables have higher electrical resistance. In 80% of the case I’d always say its the cable’s fault.