Open the Messages app on your iPhone
Find the conversation you want to save
Tap and hold a message
Tap More
Select the messages you want to download or save
Tap the Share icon
Choose Mail, Notes, Files, or another app to export the messages
Send or save the exported messages to your chosen location
Take screenshots of the conversation if you only need a visual copy
Use a Mac with Messages enabled to sync and copy messages from the Messages app
Use third-party software on a computer to export iPhone text messages
Back up your iPhone to iCloud or a computer to preserve your text messages