Hi,First, before even installing CM12.1, flash the boot.img. It's inside the CM12.1 zip file. Instructions at bottom here.
After you've done that your present bootloader will be incompatible with the present ROM (won't boot), but that's fine because you're instantly going into recovery, wipe data, cache, and flash CM12.1 then gapps one after another. Make sure those already are present on your device, or SD card, before you get here.
Now the ROM is guaranteed to boot.
However, it's not guaranteed that the modem will work appropriately, because 5.0.2 has officially come to the Xperia Z, and CM12.1 is incorporates latest SONY C6603 lollipop blobs, and I don't know whether it brings some modem firmware updates. In case you experience issues here's a central Europe .ftf you can flash with flashtool. You'll have to redo the entire process, but you'll know you have 100% CM12.1 compatibility. It's probably an unnecessary precaution, but just in case you can't make a phone call, give that a shot.
Good luck!
Okay I tried. Once I do "fastboot flash boot boot.img" and succeeds, then I cannot start device anymore.
Power button only vibrates, so no recovery too!
And last, if it helps, I have to unlock bootloader each time I try to flash boot.img. Otherwise it just says that this is not permitted.
I wonder if I should not try installing CM12.1 over Jelly bean 4.1, due to difference at partitions.
Does any of that help you understand what should I do?
Now I installed kit kat from sony, and I am waiting for help in order to retry.
Thanks
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