How to transfer apps from a previous iPhone to a new one?
you can all you need to do is use iTunes and create a backup of your old iphone, after that's dome plug in the new iPhone and choose the previous iPhone backup (old iPhone) and it should work, I have done this since the iPhone 4 so I'm sure it works. The only thing is it takes a while if you have used a lot of your memory.

You can find additional instructions on how to do this on Apple's support site.