I did it
Hello to all!
I replaced the battery successfully.
I bought a new battery offered at ebay. It was declared to use for ipod 1. generation. (as mentioned above). The width and the lenght is a little bit bigger than the original, but at last its fit, after a little modification. Look at the data shield. (pic 1)
But the best thing is: the plug fits perfect. (pic 2)
I used some adhesive strips (double sided) to fix the new battery. (pic 3)
The battery has to be mounted close to the plug. (pic 4)
Because the new battery is a little bit longer, I removed the division bar from the rear cover. (pic 5)
I hope this helps you like your hints were helpfull for me! - quit pro quo (H.L.)
Keep on reading, Thomas