Open the Messages app
Find the SMS conversation you want to save
Press and hold the message bubble
Tap Copy
Paste the message into Notes, Mail, or another app
Take screenshots of the conversation
Save the screenshots to Photos or Files
Use the Share option in Messages to send the text to yourself
Back up your iPhone to iCloud
Back up your iPhone to a computer with Finder or iTunes
Use a third-party app to export SMS messages
Save important messages as PDFs by printing from a computer backup
Keep the original conversation in Messages if you do not delete it