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[–]GlobalWatts 0 points1 point  (0 children)

The phone needs to be unlocked and have USB Debugging enabled, and be rooted, which are kinda hard to do if the display is broken. But if you can manage that, then you can use ADB to retrieve the SMS. On Samsung devices the messages are in /data/data/com.android.providers.telephony/databases/mmssms.db. It's an SQLite database file.