save a messages file

The easiest way to do it is with a dedicated application such as PhoneView (Mac) or TouchCopy (Mac or Windows). Both will allow you to archive your message conversations as pdf or text files. They are not free but are well worth the money if this is something you need to do regularly.

If your pc is a macOS, you see the Apple articles below:

Use Universal Clipboard to copy and paste between your Apple devices

Use Universal Clipboard to copy and paste between your Apple devices - Apple Support

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac – Apple Support (AU)

From the Mac, you can just copy and paste the text into Pages then print it out, or Save as . . .

Finder -> Apps -> Messages -> select a messages -> copy -> paste to xxx.

If you have multiple messages, you must select, copy & paste per message.

Form iPhone -> You can take a screenshot and print it out.

If your pc is a Windows OS, you need a 3rd party app.