Could it be simpler than that?
Method for 6.1.B.0.544 and 6.1.B.0.559 update:
Rooting via Flashtool:
1. Download Flashtool 0.9.6.0 from Flashtool Homepage:
2. Install it on your PC
3. Run the Flashtool and connect your phone (enable USB debugging first/turn on unknown sources)
4. Hit the Root button (second in row)
5. When you see "waiting for restore to finish" open your phone and run Backup&Restore app and restore RootMe.tar file.
6. Wait until Flashtool do the rest of work
Don't forget to hit THANKS button!
For those guys who dont have Backup&Restore.apk on their phones u can try to install it manually:
EDIT: Method for 6.1.1.B.1.54/6.1.1.B.1.75 update:
1. Download .zip file attached below.
2. Update ur phone via Flashtool or PCC to 6.1.1.B.1.54/6.1.1.B.1.75 update.
3. Flash .559 kernel via Flashtool. (no need for checking kernel number on ur phone if flashing is successfully done, just go to the next step)
4. After flashing reboot ur phone and use regular method above for .544 and .559 firmware.
5. When u r done flash .54/.75 kernel via flashtool and reboot ur phone.
EDIT 2: Method for JB update[LB]:
1. Root any of above ICS ROMs
2. Install OTA RootKeeper from Google Play Store
4. Start OTARootKeeper and click "Protect root"
5. Click "Temp. unroot"
6. Update JB via OTA
If this doesn't work for you try with this method.
Xperia P LT22_6.1.1.B.1.54_Kernel.zip
Xperia P LT22_6.1.1.b.1.75_Kernel.zip
Thanks to naruto20007 for kernel files!
Thanks to lebartman for first JB method!
Thanks to Pandemic for second JB method!
Please, keep this thread clean. Thanks!