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If you’re asking if there’s a way to save or export an entire conversation as a text file, there is not. You can copy individual messages and paste them into Notes or Pages, for example, or take screenshots, but both methods would be very tedious.
 
iMazing app can actually create a PDF of any one of you Message conversations. It's reasonably priced and worth every penny. It is a great ios device manager. As you can see below I have the ability to do many things with the app in regards to Messages or for that matter anything on my phone. I use this app over iTunes and will continue to do so.

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