I hit this exact wall, so hopefully this saves you the hours I lost.
The short version: this isn't something you're misconfiguring, and it's not really fixable at the agent/flow layer. The Office 365 Outlook "Draft an email" action always writes the draft to the Drafts folder of whatever identity owns the connection. "From (Send As)" only changes the sender stamped on the message when it eventually sends, it does NOT change where the draft is stored. So the draft lands in your personal (or the service account's) mailbox, never the shared one. The "Send an email from a shared mailbox (V2)" action doesn't help either because it sends immediately, with no draft variant.
The reason no connector action solves it: all the Outlook connector actions are scoped to "my" mailbox by design. The only interface that lets you address a different mailbox and write into its folders is Microsoft Graph.
What actually works, two Graph calls via "Invoke an HTTP request" (or HTTP with Entra ID):
1) Create a threaded draft reply directly in the shared mailbox:
POST https://graph.microsoft.com/v1.0/users/{shared-mailbox-address}/messages/{originalMessageId}/createReply
2) Patch in your generated body:
PATCH https://graph.microsoft.com/v1.0/users/{shared-mailbox-address}/messages/{draftId}
{ "body": { "contentType": "HTML", "content": "<your reply text>" } }
The draft shows up in the shared mailbox Drafts folder, in-thread, ready for a human to review and send. Use createReply rather than a plain POST /messages so it stays threaded , matters a lot for a customer inbox.
How I'd split it:
- Copilot Studio agent (or a prompt) does the thinking: classify quote request vs spam vs other, generate the reply grounded in your KB.
- Power Automate does the mechanics: trigger on new mail in the shared mailbox then call the agent then the two Graph calls above.
Don't convert the shared mailbox to a regular mailbox, it needs a license, you have to manage MFA/sign-in for what's really a team inbox, and you lose the delegated multi-user access that makes it work for a sales team. It doesn't get you anything Graph doesn't already.
On permissions: you can't use the shared mailbox itself as a connection (no interactive sign-in). Either an app registration with Mail.ReadWrite locked down to just that mailbox with an Exchange Application Access Policy (my pick for an unattended flow), or a service account with Full Access to the shared mailbox.
Also heads up, the Copilot-in-Outlook "shared mailbox" support Microsoft shipped this spring is a different thing (it's for a licensed human drafting in the client), so don't get your hopes up that it fixes the autonomous path. It doesn't.
Hope this helps!