1. Enable iCloud backup on your old iPhone. Tap "Settings," and "iCloud," followed by "Storage & Backup." Tap the slider next to iCloud Backup to the "On" position to enable iCloud backup. Tap "OK" on the pop-up window informing you that your iPhone will use iCloud and not iTunes for backups.
2. Tap "Back Up Now" and wait for your old iPhone to back up to iCloud.
3. Turn off your old iPhone after the back up to iCloud is complete.
4. Turn on your new iPhone and follow the activation steps. Ensure you have access to a Wi-Fi connection, which is required for activating your new phone.
5. Select "Restore from iCloud Backup" during the Setup Assistant procedure on your new iPhone.
6. Enter any passwords for accounts if you are prompted during setup to do so.
7. Tap "Settings," "iCloud" and then "Storage & Backup" to check the progress of the restore from your old iPhone backup on iCloud.
8. Tap the "Messages" icon on the home screen after the backup is restored and your old iPhone text message history should be restored on your new iPhone.
If you failed, try to follow this tutorial: https://transferphone.com/copy-sms-between-iphones.html