Unfortunately, you are very limited in what you can do with that backup. In fact, there is literally nothing you can do with an iCloud backup unless you restore the backup. This can be done, however, on any iOS device (as in iPhone, iPod, or iPad), that is at least the iOS version that the stolen device was on. For example, if the iPhone 4 was running iOS 6, you will only be able to restore to a iOS 6, or 6.1 device.
If you are on a Mac, you should have easy access to Calendars, Contacts, Notes, Reminders, and such data. If you are on a PC, you can access most of that by going to iCloud.com. This isn't really the data that you've backed up, though, and it's really data that is just "synced" through iCloud. Either way, Contacts, are typically pretty important.
If you own a Mac, you should be able to get your Photostream pictures by installing and opening Photostream. This doesn't capture videos, though.
If you do have an eligible iOS device that you can do a restore on, be sure to back up that device locally before wiping. It might also be advisable to make sure that device doesn't do a backup of the newly erased setup to iCloud. If you keep that iCloud account disabled on that device, you should have an easy restore from iCloud, and a backup in iTunes should something go wrong.
I found how to make iTunes restore only contacts, while preserving the rest intact:
- run iTunes before connecting iPhone
- disable auto-syncing in preferences:
Edit > Preferences > Devices > Prevent iPods, iPhones, and iPads from syncing automatically should be switched On
- connect iPhone to PC. In iTunes:
- on the Sidebar, select your iPhone (press
Ctrl-S if Sidebar is hidden)
- on the top central menu (
Summary | Info | Apps | Music | ...), click Info
- scroll the page to bottom, there's
Advanced section
- switch on:
Replace information on this phone > Contacts
- click
Apply in the bottom right of iTunes window (or right click on iPhone and choose Sync)
These steps wipe the local contact store on iPhone (leaving cloud contact sync alone, if applicable) and injects all the contacts stored in the PC-side data source that iTunes has selected (from Windows Contacts in my case; Outlook on Windows / Contacts on Mac in other setups) and pushes those contacts to the device. It does not load contacts from an iOS backup.
Best Answer
You would want to power off the phone immediately and then get a quote from a forensic / data recovery company if the data is worth paying for. I’m not aware of any tools to do recovery yourself, but perhaps someone else has that answer or an explanation why that’s not viable or cost effective.
There are going to be all sorts of scam software, so here are two reputable companies that do recovery. One says they work with iOS, the other does not but I trust them for Mac recovery and they might have some recommendations worth exploring.
Since iCloud has a deleted photos album, be sure o check that as it works even without an iCloud backup. Sorry you’re in this place, too late to make a backup when the data is already gone. Try not to lose the lesson now...