How to back up my text messages from iPhone to computer

when connecting your iPhone to your computer, head over to iTunes and make a backup. Make sure you're backup on your computer not on iCloud. Please visit this Page where you find the necessary informations about viewing saved text-messages:

How to Backup iPhone SMS to Your Computer - Hongkicat

Hope this helps :) Cheers

moesphemie


You should check out the app iExplorer and export the texts without iTunes, in a variety of formats directly to your computer. You can export many other files as well, including app data, photos, movies, etc. It can also open iTunes backups to extract files you may have deleted accidentally, mitigating the need to restore the entire backup.

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