MAKE A BACKUP !!!
1.1 You need obviously an already rooted phone with [NUT]'s Dual Recovery with a previous firmware version (4.4.2)
If you don't have the recovery, you can install it only on version 4.4.2 from here: [Z2][TWRP][PhilZ Touch][CWM] XZDualRecovery Q&A see post #2 for instructions. Do not use this recovery for 4.4.4 because root won't work! Use the patched version below.
1.2 You need Flashtool with working USB drivers (Make sure flashmode works - which means the drivers are properly installed on your system - before you start with this tutorial).
2. Download the new FTF update file for your phone/branding. Use the same customization version (xxxx-xxxx) that is on your phone now!
This you can do with Flashtool (Devices/Check Updates menu) or download it from the [FTF] STOCK FIRMWARES for Xperia Z2/Z2a (D65x3/D6502/SO-03F) thread.
(Alternative option for advanced users: XperiFirm -> you can create an FTF from the downloaded firmware files with Flashtool.)
3.1 Download PRFCreator v0.5.zip from [TOOL] PRFCreator - easily create pre-rooted firmwares. (DO NOT USE v0.6! IT DOES NOT WORK!) v0.7 may work though, I couldn' test it. But you are always safe with v0.5.
3.2 Download latest stable SuperSU update package from here. (Advanced users can try the the latest BETA SuperSU package from this thread Read the changelogs and the beta thread carefully, you may get into bootloop with latest versions)
3.3 Until [NUT] fixes the rickiller installer script, download XZDualRecovery's latest patched flashable version from here or from the attachment. You have 4 files so far:
D6503_23.0.1.A.0.167_Telekom_HU.ftf (with different name)
UPDATE-SuperSU-v2.xx.zip or BETA-SuperSU-v2.xx.zip
5. Load the FTF, SuperSU and XZDualRecovery (flashable!) zip files into the three section.
6. Uncheck all the Include options [ ], we don't need them, we will flash them with Flashtool after the update. I think it's still safer to flash kernel, baseband, boot and other system critical parts of the firmware from Flashtool.
(But if you want to include them anyway then you can skip part 11 and start your phone normally.)
7. Push Create. After it's finished (wait for the Create button to be available again), you'll find a flashable.zip in the folder of PRFCreator.
8. Copy flashable.zip to the internal/external SD card of your phone.
9. Boot your phone into recovery (TWRP recommended).
10. Install flashable.zip in recovery. After finished DO NOT REBOOT !!! Clear Cache/Dalvik only and go back to Home and choose Reboot/Power off.
11. Start Flashtool and with the Flash device icon flash the kernel and other baseband files from the FTF in Flashmode.
Use the following configuration (or similar):
[ ] APPSLOG [ ] CACHE [ ] DATA
[ ] BOOTBUNDLE [x] PARTITION [x] TA [ ] KERNEL [ ] FOTA [ ] BASEBAND [x] SYSTEM [ ] ELABEL
[x] No final verification [ ] Reset customization
Push Flash button.
Push the Volume down button and connect the USB cable to the computer's USB port. Wait until Flashtool begins with the flashing and you can release the Volume button now.
When finished, unplug the the phone, start it and wait until it completes the first boot. After it is fully working, check SuperSU and if you can mount system R/W too.
ENJOY another rooted version of Android I can give support only for this process, for the tools you need to ask your questions in the appropriate threads above.
Thanks to @zxz0O0 for creating the PRFCreator, it makes things easier in this process (you don't need to mess with linux mounts, virtual machines and other scripts copying system images and recovery updates to a zip).