Save 1-1 chat for future sharing
I had to tell the user to do this instead; 1) Use Skype IM instead of Team chat 2) Ctrl-S to save chat to Outlook 3) create a folder structure matching your team structure in Outlook or OneDrive 4) drag the msg into the folder. The admin setting to save Skype chats to email needs enabled for the above to work.
Stuart McBain commented
Suggest a feature like "CTRL +S" could work similar to what happens if you add a extra person to the chat today. You get a pop-up box asking how much of the conversation you want to save but then either saves it to Outlook (like SfB) or simply downloads is a PDF
The option to fence 1-1 **private** chats within a team or channel might be the essence of the request before it's shared and represents 'filing' mainly. For actual sharing, there's the issue of storage and the decision whether to have Teams store and manage the chat or to just allow users in that chat to save out to Outlook or OneDrive. Or Sharepoint.