You can send private notes within conversations from the shared inbox.
Private notes are a special message type only visible to operators and unique to each conversation. Use them to share messaged between operators in the log on messages in any conversation.
To send a private note, when viewing a conversation in the inbox switch to the "Private Note" tab on the top of the message composer. You'll notice that the background of the message input changes to yellow. Type your message and press enter.
To revert to replying to the visitor, press the "Reply" tab and ensure the message input changes back to white.