How do I transfer data and everything (SIM/Data, SD) from my old Sony Xperia Z3 to my new iPhone 5s?
The screen doesn't work on my Sony, but that's the only thing..
It's still alive, alarming etc. it's just impossible to manage from the screen, it's impossible to see anything
iPhone 5s, null
If you cannot navigate through your Sony, you won't be able to use Move from Android to iPhone, iPad, or iPod touch - Apple Support.
SIM cards carry no information anymore other than the identifier for your service with your carrier. That SD Card will be your only chance of recovering anything outside of accounts, but you will need to do so through a computer. I'd recommend popping it into your computer, grabbing what relevant information you can, and then syncing it to your iPhone from iTunes syncing.
Sync your iPhone, iPad, or iPod touch with iTunes on your computer using USB - Apple Support
Keep your photos safely stored and up to date on all your devices - Apple Support
A lot of information like notes, email, and contacts are now managed by our various email services. Sign into all of your email accounts on your iPhone through Settings>Mail, Contacts, and Calendar.
How do I transfer data?
