In situations where you need to loop a third party (someone who is not an agent in Groove) into a conversation, you can do so by forwarding the conversation. 

To forward a conversation click on the '...' in the top right corner of the reply editor. 

This reveals more details about the conversation and you can switch to forward by clicking the reply options on the left.

When you forward a conversation out of Groove, it will include the entire thread up to that point, so the recipient of the forward will see the full context of the message. 

(Please note it is not currently possible to edit or remove parts of the previous thread being forwarded.)

Then when the third party recipient replies to your forward, this message will be threaded into the Groove conversation chronologically.

Forwarded messages are displayed with a green background to visually indicate that they are forwards and differentiate from the white background of regular replies and the yellow background of internal notes. 

Forwarded messages and replies are completely private, they will not be visible to the end user when you reply back to them.