I see. So if you have three capacitors in series, the energy to charge the middle capacitor flows through the outer capacitors. If energy does not flow through the outer capacitors the middle capacitor will not be charged. If energy does flow through the outer capacitors the middle capacitor will be charged.
At no point in time any energy flows through the capacitor.
3 or more capacitors in series are no different from a single capacitor.
If all 3 capacitors are 1000uF when connected in series will look like only a single 333uF capacitor.
Imagine a parallel plate capacitor with 5mm between plates and say it has 1uF capacitance.
Then insert a very thin 0.001mm plate between the two plates with same area. This will be the equivalent of two capacitors in series so from outside the capacitor will still look like a single 1uF capacitor (just slightly more due to that 0.001mm reduction in distance between plates).
If that plate is instead 2.5mm thick then from outside it will look like a 2uF capacitor but it is actually two 4uF capacitors in series.
Adding multiple plates will not change the fact that from outside any number of series connected capacitors will appear as a single capacitor and it can be charged.
There will be a current flow inside the middle plate as electrons from one side of the plate travel to the other side (it is a short distance even for the 2.5mm thick plate) but there is still a current flow as electrons that where already there travel from one side of the plate to the other while capacitor is being charged.
This charge separation remains there after you remove the battery so it is stored energy not used energy. Now this capacitor or series capacitors can be used to do any sort of work you want with that stored energy.