Simply run the above on your computer, plug your iPhone in and once you see your iPhone notes, click on the "Export selected" button.
This short video shows more about backing up your iPhone notes to prevent losing them in the future:
Lost notes - need to recover iPhone notes:
Recover notes with iTunes
If you have already lost your notes, here is the method recommended by Apple to recover your iPhone notes:
1. Run your iTunes and navigate to Edit > Preferences (on Windows) and iTunes > Preferences (on Mac).
2. Now, go to the Devices tab and make sure to check the “Prevent iPods, iPhones, and iPads from syncing automatically” option. This way you will make sure that iTunes ill not try to delete any data from your iPhone such as your songs or videos upon sync
3. Now connect your iPhone to your computer and with your iTunes open, navigate to the Info tab. Scroll down to Advanced and check Notes under “Replace information on this iPhone”. Finally, click on Sync
Recover notes without using iTunes
iTunes only keeps a single copy of your iPhone backup. This means that each time a new iPhone backup is made, iTunes overwrites the previous one. The risk of iTunes accidentally syncing and backing up your iPhone, essentially overwriting the original backup containing your notes is real. To avoid this risk, restore the original iPhone backup made by iTunes without even having to run iTunes. To do so, use CopyTrans Shelbee which is a free utility that can restore the latest iTunes backup to your iPhone.
1. Download CopyTrans Shelbee
2. Start CopyTrans Shelbee and connect the iPhone. Select "Restore"
3. Click "Choose" and from the newly-opened window, select the original backup containing your notes
4. Click "Start" to begin the restore
5. CopyTrans Shelbee restores the iTunes backup containing your notes back to the iPhone
For a YouTube video showing instructions about how to recover your iPhone notes, have a look below:
To back up your iPhone notes safely in order to prevent losing them again in the future, please have a look at this page.