At one stage, not at my choice but appreciated,, my messages were showing in my email in-box. Couldn't find it for you Googling around but not knowing what you want, there are heaps of ways to transfer messages by, for instance, backing up to email, etc. You should be able to find something to meet your needs. Other users plesse add suggestions.
Aside from taking screenshots of the message and convert to other format like PDF, I don't think there's an out of the box option to do this.
There are 3rd party apps that says they can export your SMS,, but I wouldn't trust them. Be careful trusting 3rd party apps that can access your SMS specially if you are using your number as 2FA for your logins.
