Follow steps for recover deleted text messages iPhone.
Launch iTunes Software from your computer
a) Connect your iPhone to the computer via the USB cable and select it from the iTunes sidebar or at the top right of the screen if you’re using the new layout.
You should be able to see below screen
b) Take Backup to your computer without encryption using iTunes Software in your Mac or PC
You should be able to see below screen.
Note: – Anyone can back up your iPhone/iPad with iCloud. However, it will not save the backup file you need to extract on your computer. By use iPhone SMS Backup tool can easily recover deleted text messages iPhone of your device to your computer instead of iCloud. After using iPhone SMS Backup, you can go back to the usual iCloud backup.