The magical recovery of iPod's battery didn't go too well. It worked for two days then it went back to the sorry state it was before. Fortunatelly the new battery arrived by mail and it was time to install it. This are the photos of the two day event that happend right there at work.
The start: iPod, new bettery, tools and a mini manual
Taking the iPod appart is a snap. Pull of the white plastic on the top, unscrew two mini philips-head screws and gently pull it appart.

If you don't open the bottom (you should pull off the white plastic and use sharp object to remove the metalic cover. Then gently unplug the wheels contact. Or else... you have a problem we had. The contact didn't detach itself but the connector did. Not good!
Some glue and a steady hand (thanks, Dane!) with a precise soldering iron and in no time the contact was back where it should be.
It was tense and we had some luck, so don't get yourself that far. Open the bottom, please.

Here it is. Playing again...
So far, the story has a happy end. For some 20€ I have a new battery that after couple of days last longer than the original did when it was new.