iMessage: how to save a string (like one saves a photo)

What is it you're trying to do?

There's no inherent support for saving messages outside of the Messages app (where the messages are actually stored in an underlying database format).

There's limited options for exporting this data on the phone itself.

Understanding your goal might help devise a solution, but as it stands, there is no direct way to save a message thread as a text file, if that's what you're trying to do.

As Camelot stated, there's no way to save a Message (like saving a photo).

When I need to save one, I take a screenshot.

https://www.lifewire.com/save-text-messages-on-iphone-5207193