Wanna extract and export the latest iPhone SMS as a CSV file to your computer, no matter it's out there or deleted? An
iPhone Data Recovery [joyoshare.com] can handily make it! It is Joyoshare iPhone Data Recovery. I used it to find, preview and recover my lost data to save on my computer as a CSV files. It is able to export both the existing and the deleted as you wish. Not only SMS, but also other data types, such as notes, calendars, reminders, call history, bookmarks, etc. can be supported.