Business Notebooks

Hi all,

I own a Probook x360 435 G8 and a HP Pro Pen G1.  The pen worked fine with my device.
More than 2 years ago, the touchscreen stopped working and eventually the notebook had to be repaired (see https://h30434.www3.hp.com/t5/Notebook-Video-Display-and-Touch/Touch-screen-stopped-working-I2C-HID-...  ) and everything worked fine again.

The touchscreen is still working fine with my fingers. However, since more than 1.5 years I had not used the pen. A few weeks ago I tried, but then pen was not working anymore. I changed the battery of the pen and even bought a new pen. Still not working, so the notebook is definetly the cause of the issue. I am using windows 11.
I also tried booting a USB-Linux: Touchscreen working, but not the pen.
Also in BIOS: Touchscreen working, but not the pen.

Any ideas how to geht the Pen working again? Is this a hardware issue or a driver issue?
I also cannot find the digitizer-drivers for my probook on the hp website. For most other notebooks I can easily finde the drivers, but not for my probook. Maybe these drivers are missing?

I also tried to bluetooth pair the pen, but the pen does not show up in the list of bluetooth devices when I try to pair new devices.

Of course I have used the HP Support Assistant to update all drivers (System, BIOS, ...) but I cannot get the pen to work again. 
I appreciate any help.

Best regards,
Harry