The battery doesn't work perfectly and was old. Also the new iPod battery that ifixit sell have more mAh so I've decided to change it.
The repair was long and I was been careful. At the end the iPod worked perfectly and the battery give me more hours.
I have an important advice about the ground strap: I've read that somebody asked if that ground strap was required: no! I lost it but I have repaired the iPod without problem.