Change IPhone and iTunes accounts?

My mum wants to use old IPhone 3GS, it's still linked up to my account however I want to stop this and change it into her own, how do I do this without me losing everything on my iPhone 5? So basically change the phone from my name to her name with the accounts being completely separate?

Simple.

Set up a NEW account on iTunes for your mum and then when logged onto it restore the phone to factory settings and start it as a new phone.

Your phone will still have your iTunes account on the computer but you NEED to remember both of you need to sign off after syncing the phones so next time either of you want to sync you have to log onto your iTunes account.