Finally I got it!
What I did this evening:
I did a download from http://distro.ibiblio.org/puppylinux/test/xenialpup/
This file: xenialpup64-7.0.7.iso
From this iso-file I build up a new bootable USB-Flashdrive. And it worked out of the box. The X-desktop runs fine and all network adapters were detected
I made the configuration for my WIFI at home and now I can use my new Lenovo X250 with Puppy and WLAN.FANTASTIC!
But: the only thing I changed was the version of puppy. Two days ago I used Puppy Xenial in version 7.0.4, today I used version 7.0.7. This was just done by accident because i killed a directory with some .iso-files.
Life can be mind bogging.
Special thanks to all, who tried to help me. Very good community here!
Best regards
Thomas_de