It's not possible to share an existing conversation to another shared mailbox - you can only move it which is not always appropriate. For example the accounts mailbox might need to be included in a conversation about a payment for an order being handled by the sales team. It is relevant to both teams and so should be in both mailboxes.
I note that if a customer emails 2 shared inboxes then the conversation does appear in both of them, so the functionality is almost there.
Your idea is now live and open for voting.