Teams "share to Outlook" feature

No the Microsoft Graph API does not have this feature directly.

I'm intrigued to understand the scenario. The API does have the ability to send an email on behalf of a user and you can make the body of this email whatever you want. You could read the body of the chat or channel message and then use sendMail to send it.
I'm betting that is what the Teams UX is doing under the covers anyway.

Am I missing something with your ask?

One scenario I have in mind is archiving. Today I can archive files or emails outside of Teams and later give someone read access (think audit or ediscovery). I cannot do that with conversations unless I convert them to a standard format.

Converting to email sounds like an option, especially as the great "share to Outlook" feature keeps all content (including images) and replies.

Today I can easily read the body of a message, just as you say. But I haven't gotten to a point where I also grab the images, the replies, and the replies' images. "share to Outlook" packs all that in a single command!