How do you transfer text messages from an old iphone (4S) to a new iphone (6)?

Howdy Ranismith,

Thanks for using the Apple Support Communities.

If you'd like to transfer the content from your previous iPhone to your new one, you can back up your iPhone 4s using iTunes, and then restore that backup to your new iPhone 6. This will restore all messages which are stored on your iPhone 4s to your iPhone 6.

Make a backup using iTunes

1. Open iTunes and connect your device to your computer.
2. Save content that you downloaded from the iTunes Store or App Store by clicking File > Devices > Transfer Purchases.
   
3. Click File > Devices > Back up.
   
4. After the process ends, you can see if your backup finished successfully by clicking iTunes Preferences > Devices. You should see the name of your device with the date and time that iTunes created the backup.
   

How to back up your devices using iCloud or iTunes - Apple Support

iTunes

1. Connect your device to the computer that you stored your backup on.
2. Open iTunes. If iTunes tells you there's an iOS update, get the latest version.
3. Choose your backup by going to File > Devices > Restore from Backup. Look at the date and size of each one and pick the most relevant.
4. Click restore and wait for the process to finish. Your device will restart and then sync with your computer. Stay connected until the sync finishes.

Restore your device from an iCloud or iTunes backup - Apple Support

Take care,

Alex H.