Can I Export a Text Conversation From My iPhone?
However, a couple of workarounds let you save and send your messages somewhere else.
How Can I Save My Text Messages From My iPhone to My Computer?

Since there is no built-in, you’ll need to save them in a different format.
You may need to take multiple screenshots if you’re trying to capture a long message thread.
Don’t worry if you miss tapping on the screenshot image before it slides off the screen.

The screenshot is in your camera roll.
Choose the method you would like to use to share your photos, in this example,Mail.
Once you’ve filled out the recipient information on the email, tap theSendicon to send the message.

How Do I Export an Entire iMessage Conversation?
Open a text message thread and long-press on the message you want to save.
If you only want to save one message, tapCopyin the menu that appears.

However, if you want to save multiple messages, tapMore.
All of the messages you’ve selected will be automatically pasted into a brand new message.
Tap and old in the body of the message, and when the menu appears, tapSelect all.
Once you’ve pasted the messages over, tap the three-dot menu in the upper right corner.
Then select where you want to export the document to.
Is There a Free Way to Export Text Messages From iPhone?
Then you’ve got the option to add your email address and send the message to yourself.
FAQ
You canexport contacts from iPhone as VCF or Excel CSVusing an app or iCloud.
After locating your phone in iTunes, import the pictures using the Photos app.