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That is because it is syncing with your iCloud account. On the iPhone 4S, go to Settings > iCloud and tap Sign Out. Tap Delete when asked. This will sign out your iCloud account from it. Then go to Settings > Mail and remove your email accounts from there.
Then go to Settings > iTunes & App Store. Tap your Apple ID and tap Sign Out.
Then go to Settings > Messages > Send and Receive and delete your IDs from there. That's it.
If you would like to delete all the contents from that phone and setup it like new phone, then all you have to do is, go to Settings> General > Reset and tap Erase All Contents and Settings. This will delete everything from it including your accounts and start fresh, so he can register it with his account.
If you have any questions or would like any additional information, please don't hesitate to ask.
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Are you sure you did all the steps correctly ? I can virtually guarantee that if you do the steps correctly, it will definitely work as your contacts are synced via either iCloud or Mail accounts. Messages and Facetimes calls only go through your IDs and the above instructions are to remove them. But you have to make sure your accounts details are deleted from that phone.
I'd recommend to erase the iPhone and then you can give to him which is more easy. This way, he can register it with his account, so your data will not go to it. To do that, go to Settings > iCloud and sign out from it. Then go to Settings > General > Reset and tap Erase All Contents and Settings. This is what even Apple suggest when you give away your phone.
Please don't rate me bad or poor or OK if you are not satisfied. Only rate the answer after we've solved the problem and I will stay with you until the issue is resolved