First idea was to install debian linux but the debian installer does not provide any functionality to resize the partitions. And without this, the windows partition will be erased after the installtion.
I knew, that the ubuntu installer had this functionality, so i created a usb stick and tried installing ubuntu.
The installation went through like a charm, but the next reboot does not show up the grub boot menu. The laptop started without any call back.
I found a solution here.
You have to enter the BIOS/UEFI and set a password:
Then walk to grubx64.efi via HDD0 -> EFI -> ubuntu:
New you can change the boot order and move the grub to the first entry: