Lithium batteries are a bit finicky, they self-discharge, and the rate varies from cell to cell, so if you have three cells in series at 4V, some of them will drop in voltage faster than the others over time

When you then charge them in series like that, it’ll charge until the three cells combined are at 12V, but that might mean that one is at 4V, the second is 3.9V, and the last is 4.1V

This drift keeps happening over time, and eventually one cell will end up at a dangerously high voltage, potentially catching fire

That’s why with lithium batteries, you need a monitoring circuit that keeps the voltages of the cells balanced

So i would not advice you to simply swap them in like that, you could charge the cells in an external charger and then use them in the device, but remove or isolate the 12V supply so it doesn’t charge them while installed

NiMH batteries might be a better fit, they basically self-balance i believe, but you’d need 10 cells in series to reach 12V