Add or Remove Association From Conversation
Currently, if you want to add or remove an association (Customer, Company, Ticket, Deal, etc.) in Conversations, you have to select on the associated contact, navigate to that conversation, and make the change. If the conversation is already associated with a ticket, you can also do this from the ticket. However, from the Conversation inbox, there is not a simple way to add Associations. If a new contact comes in you can associate it with an existing Ticket, Customer, Company, etc. from the Conversation inbox. I believe this used to be something that was allowed on earlier beta/alpha versions of HubSpot.
You can change associations from Conversations if you expand the "Email detail" box to have the email box detach. But adding/removing the associations will only save if you send the email. Again, none of this is simple.