Use Google Messages backup and restore
Turn on Google One backup on the old phone
Back up SMS and MMS to your Google account
Sign in with the same Google account on the new phone
Restore the backup during new phone setup
Use Samsung Smart Switch if both phones are Samsung
Use the phone’s built-in transfer tool during setup
Use a third-party SMS transfer app
Export texts to a file on the old phone
Import the file on the new phone
Use an SMS backup app with cloud sync
Move the SIM card if only carrier messages are needed