Syncing iphone to blank itunes library after authorizing computer

My mum has never synced or backed up her phone to her laptop. The laptop has never even been authorised - the phone has only ever been used on its own and with the app store and itunes store on the actual phone.

She is now trying to transfer everything from this phone (a 4) to a new one (5c). The trouble is that even though I've authorized the itunes library for her phone and her iTunes account, when I plug the phone in it only gives me the option to set it up as a new phone, or restore from a previous backup (my dad's phone). It doesn't give me the option to back up what's already on the phone, which includes photos, texts, etc.

How do I do this?