Despite the title saying "charger pcb" this board look like it's a simple BMS that will do the following :

• Protect the cells from over current (this board is rated for up to 40A) and shorts
• Protect the cells from over charging (usually limit voltage to 4.25-4.30V/cell but not always very acurate)
• Protect the cells from deep discharge (a typical low voltage limite for this kind of board is 2.7-2.8V)
• Try to keep the cells balanced during charge

But it won't limit the charge current and the over charge limit is somewhat high so you need to use a CC/CV charger with a CC (current) setting matched with your cells recommanded charge current and  a 4.20V limit (or lower if you agree to trade some autonomy for longer life)

Note : Beware that powertools require high current batteries

You need a balanced RC charger, which support 4S Li-Ion.

I did the same with two cordless drill.
—> Be aware that after the rebuild, the drill will fall over easly, because the batteries are lighter!

I’m not sure, if the board can balance. Usually the balance current im ma should be indicated.

The four 43 ohms resistor (with 430 written on it) on the left of the picture are balancing resistors.

But who knows if the picture is accurate ...

The last link shows (edit : ) nearly the same board from an other seller

1. Yes you can. It will work fine, especially if you only use new cells, but the BMS will be only the only thing to trust that the battery pack is fine.

If possible I would add this:
https://www.aliexpress.com/item/F00872-Low-Voltage-Buzzer-Alarm-Volt-Met...

Quite nice, and allows you to check the individual cells voltages, and if the BMS cuts off at the right voltage.

2. If I were you, I’d pick a 24V charger/laptop power supply, and wire a buck converter with adjustable CC/CV, and set it 16-16,4V for much higher cycle life, like this:

https://www.aliexpress.com/item/Lithium-Charger-Step-Down-Power-Supply-M...

It’s really nice. You can adjust the current so you can do a slow charge at 1A, a fast charge at 3A, and if you put a heatsink on it, super fast charge at 4A.

Hope this works out for you. If it doesn’t you could always convert it to a 12v car plug or gator clips and throw in you trunk.
Not as portable. But they work in an emergency, I had one in my last RV with some old drill bits and a few screw tips. Came in handy a few times.

From the title I thought you were going to adapt a lithium battery pack and charger from a newer drill to fit your older drill with an adapter.