I got a bit confused. To install for "GALAXY S III Neo GT-I9301I" an upgrade to "Galaxy S3 NEO CM12.1 Lollipop = Android 5.1. ROM" I found two different methods an I wonder what are the best or which is correct?
(there other things like backup i.e select the right ROM etc I have done now it comes to the installation)
I could takte this way:
 Copy the Coustom ROM "cm-12.1-20150518-UNOFFICIAL-s3ve3g.zip" to your SD card
 Copy the GApps file "open_gapps-arm-5.1-stock-20190924 (32bit).zip" to your SD card
[x] Create a Nandroid backup
 Go back to the home screen and select Wipe.
Swipe the bar to reset your phone (it won’t wipe your internal storage)
 Return to the TWRP home screen and select Install
Navigate your way to where you saved the ROM (the zip file).
Tap the zip file to select it
Swipe the bar to begin installing.
 After it completes, repeat steps to install the GoogleApps (GApps) zip
if you want.
STEP 1: Put your phone into download mode.
STEP 2: Open the ODIN application on your PC.
Connect your phone (while it is still in the download mode)
to the PC using a USB cable.
ODIN will show an "Added! message" on the message box.
And 0:[COM3] above
STEP 3: Click on the [AP] button on the ODIN application
and select the <i9300i-cwm-126.96.36.199_v1>.tar.md5 file.
STEP 4: Select the appropriate options before flashing the recovery image:
only the [x] "Auto Reboot" and [x] "F. Reset Time"
Make sure all other boxes are un-checked [ ].
STEP 5: Select the start button, which will start the flashing process.
When you get the PASS message,
then your phone will reboot automatically.