Does your shared inbox also share the AI conversation?

Two people can work from the same inbox without seeing the same AI conversation. Microsoft's current Outlook documentation says Copilot Chat supports shared and delegated mailboxes, but conversation history stays tied to each user's primary account. Other people using the shared mailbox cannot see it. The same page says drafting and summarizing are supported; sending, email triage and meeting changes are not yet supported there. This is documented behavior, not a rollout I have tested. Imagine a rep using the chat to work through a disputed refund, then leaving for the day. The customer emails again. Their cover can read the email thread, but not the rep's AI discussion. I would ask the rep to leave the checked conclusion, relevant policy link and outstanding question in the team's existing case record. No need to paste the whole chat or make every draft permanent. Just save what the next person needs to continue. Before buying this for a shared support inbox, try covering one case without asking its original rep for help. Does the useful context stay with the customer, or leave with the person who asked the AI?