If you are switching to a new iPhone, or just want to have a backup of your old messages, you can back up your iPhone messages to your computer or to iCloud.
To back up your iPhone messages to your computer, you will need to have iTunes installed on your computer. Connect your iPhone to your computer and open iTunes. Select your iPhone in the iTunes sidebar, and then select the “Summary” tab. Scroll down to the “Backups” section and …
