Sylvain, when I experimented with with electrolysis I used an old computer power supply unit. Perfect would be an old AT type one but newer ATX ones work too.

Yes voucht I do believe that connecting a battery and charger will work.
Not done that myself as lucky to have an old charger but have seen others do that.

I really don't get the point in a battery charger that can't charge a dead battery.

Yes, totally agree, I hate this electronically over-controlled devices!

Madis, I unfortunately don't have an old computer (well, yes, I do have an old computer, but I'm using it :D ). I could go to the recycling centre close to here, and try to find one there, but I tried with the donor battery (thank you shorty for the answer), and it works perfectly.
Thanks again guys!