I did, but doesn't work, hence the request for help.
So what I am doing is:
Open Terminal and type:
sudo rm -Rf /Library/Extensions/RealtekRTL8111.kext
(type password)
then:
sudo rm -Rf /System/Library/Extensions/RealtekRTL8111.kext
then:
sudo kextcache -i /
after the process has been done, I restart the computer.
Once started again, I double check there is no RealtekRTL8111.kext inside the folder Library/Extensions.
From here I tried different ways:
1. Installing the once working driver from Multibeast, then "sudo kextcache -i /" and restart.
The Ethernet port is not back in the System Preferences.
The RealtekRTL8111.kext is present inside the Library/Extensions
Redo the Terminal codes.
2 Using KextBeast I install the new driver downloaded from the Github:
https://github.com/Mieze/RTL8111_driver_for_OS_X
then "sudo kextcache -i /" and restart.
The Ethernet port is not back in the System Preferences.
The RealtekRTL8111.kext is NOT present inside the Library/Extensions
Redo the Terminal codes.
3 Type
sudo cp -R RealtekRTL8111.kext /Library/Extensions
and I get:
cp: RealtekRTL8111.kext: no such file or directory
the new driver's folder is present either on my desktop and my Download folder.
then "sudo kextcache -i /" and restart.
So it seems the only way to install the .kext here is through Multibeast, even if is still not working.
So I re-done the phase 1 again so at least I know the driver is present in my system.
New files attached.