Can I transfer a backup from a iPhone 4 to a iPhone 4S or iPhone 5?

So I've been using my iPhone 4 for around a year now and I just lost it last week, so I got a new iphone and I was wondering, since I can't sync to get a new backup as my iPhone 4 is already lost, so is it possible to somehow use a previous backup from previous syncs and sync it into the new iPhone? Sorry if this sounds really complicated, really had a hard time to phrase it properly.

Yes. That's possible.

Yes, that does sound quite complicated but it is possible. If you plug your new phone into your computer, it should ask you if you want to set it up as a new phone or restore it from a backup, I would just select Restore from previous backup of your old phone.

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