On the one hand, the HubSpot Knowledge Base article on connecting your personal email says “you cannot connect Office 365 shared mailboxes to HubSpot”.
However, elsewhere the website advises that if you want to connect a Microsoft 365 shared mailbox to HubSpot, you should:
- Set up a hosted email address in HubSpot
- Add the hosted email as a forwarding address in Microsoft 365’s settings.
Full details on the process are given in the article “Forward emails to a hosted email address in the conversations inbox” here:
I haven’t tried it yet but I’m hoping it’s the answer.