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Is there any way to move installed apps to SD card or install apps on SD card in Xperia Z?
No unless you root and partition your SD card

Android its killing the SD card
I am Iranian and I do not speak English
Please complete explanation 
Hi, as uliwooly says....no you can not move APPS to your SD Card......it is not a Sony/model restriction but an Android/Google restriction 
Android doesn't support this feature anymore, hence, you will have to root and partition your SD card.
Thank you all
Anytime