1.Click Phone Backup on the left pane. Move the mouse to Selective Backup, and click Get Started.
2.Under General tab, click Back Up Now button to initiate a full iTunes backup on iPhone.
3.Double-click the message icon and uncheck the messages you don’t want to backup, then click OK to return the main page.
4.Click Back Up Now button. Remember that iTunes does not allow you to back up the messages or certain data you want.
5.Go to Settings, tap on the user profile at the top of screen, choose iCloud.
6.Click Export to Computer icon from the toolbar at the top to backup your iPhone text messages. Choose a format to save your messages as CSV, HTML, or TXT.
7.Click Backup Storage Path to choose a location to save the backup files on your computer. After that, click Start Backup to start the task.
8.Scroll down to Backup and turn on iCloud Backup, then tap Back Up Now option. After that, just wait unless the process ends.
9.Download, install and run FoneTool > Connect your iPhone to computer using the USB cable, enter passcode on screen when asked.
10.Download and install the latest version of iTunes. Connect your iPhone to computer, unlock it and click Trust This Computer if needed.
11.Open your iTunes, click the iPhone icon and go to Summary. Then tick This Computer and click Back Up Now. Just be patient and wait for the final result.