Will I be able to recover these photos? (iPhone)?

I have photos saved on my iphone 4 inside a privacy app. The phone is now broken and i can't get to them. I have backed up the phone to my computer, and I'm getting the iphone 5s. If i set up the new iphone to the backup of my old one (if i can even do that) will my pictures still be inside the privacy app?

You can certainly transfer your old iPhone photos to your new iPhone 5S from the backup and the backup will still be where it was. And you can backup your iPhone to computer use a professional data recovery for iPhone. That is, after you backed up your iPhone to computer, all the files can be accessed directly from the location you saved it.

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