It’s no need for special Alienware drivers, just like the links says , add few line in the driver file. Something like this
/* Dell */
{ USB_DEVICE(0x413c, 0xb097) },
if so, what do I need to execute in the following so the kernel will be notified about this change? Or shouldn't I touch the file "/usr/src/linux-headers-5.19.0-31/include/linux/usb/r8152.h" at all and instead ....
*** EDIT ***
I made a successful progress, however I need assistance from a pro to verify if this is the correct way to go. My goal was to add the identifier 413c:b097 to the kernel module r8152. Unfortunately I had no source file r8152.c on my filesystem. I ran "apt install linux-headers-5.19.0-31 && updatedb && locate r8152.c" but still no "r8152.c" found under /usr/src/* where I would have expected it. I also tried "apt install linux-source" but still no success. At the end I downloaded the file from <https://git.kernel.org/pub/scm/linux/kernel/git/netdev/net-next.git/plain/drivers/net/usb/r8152.c> and saved it under "/usr/src/linux-headers-5.19.0-31/drivers/net/usb".
$ modprobe -r r8152
$ ls /usr/src/linux-headers-5.19.0-31/drivers/net/usb
Kconfig Makefile r8152.c
At the end of file "r8152.c"