I found something and now I have internet via DHCP !!! ;)
The problem was that after booting obarun-minimal ISO (net-installer) the DHCP got something wrong. After reading the contents of /etc/resolv.conf I found:
domain fritz.box
Then I looked at Arch (is currently installed on my system) and /etc/resolv.conf shows the variant:
search fritz.box
nameserver: xxx.xxx.xxx.x
Then I have this content after booting obarun-ISO with the command:
sudo nano /etc/resolv.conf
replaced with the content (saved in buffer) and everything works as it should.
The obarun-installer now finds internet. ;)
But haven't installed yet, I'll obviously do that tomorrow.