IOS – iPhone 6 back up to iPhone 7 without photos/videos

All you need to do is plug in your iPhone 4 into the Mac, and depending on your setup, iTunes should start backing it up. The Mac isn't actually a requirement here, if you set up the iPhone 4 with iTunes on a PC, you can do the same there.

When you get your iPhone 4S, and plug it into the computer, it will ask you if you would like to set up the phone as a new phone, or use a backup from a previous device, like the iPhone 4. Say yes - to use the backup - and it should set up the 4S just like your 4.

With iOS 5, iCloud actually will do part of this for you as well. If your iPhone 4 is already backing up to iCloud (instead of iTunes), when you set up iCloud on the 4S, it may ask you if you want to set it up using the previous backup. This is exactly how I migrated my wife's iPhone 4 to a 4S when she got it.

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.