I bet you can do it.
I converted an old spot light I got back around 2000 from lead acid to LiFePO4. But I have not tried to charge it yet.
It had a 2.5ah 6v acid battery. Now it has 8ah of lithium stuffed in it.
I don't know if the laptop top lithium ion are suitable for drill use. I know something like LiFePO4 would be.
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