You do not have to move any mail history, and your customers do not have to learn a new address. The switch is a forwarding rule plus about twenty minutes of setup.
Your portal is assigned its own address, usually [email protected]. Leave your existing shared mailbox exactly where it is and forward it to that address. Customers keep writing to the address they know, and every message arrives as a tracked ticket.
In Microsoft 365, open the shared mailbox settings and add forwarding to your portal address. Two things catch people out here:
Shared mailboxes usually carry unwritten rules - folders for billing, someone who always picks up technical questions. Create a group per team under Settings > Groups and assign the agents who were already doing that work. If different teams need their own address, a group can carry its own.
Do not import history. Leave the old threads where they are, answer new tickets in the helpdesk, and after a few weeks the mailbox stops receiving anything that matters. Migrating years of mail creates thousands of closed tickets nobody reads.
Send a message from a personal address, confirm it becomes a ticket, reply, and confirm the reply arrives in the inbox rather than the spam folder.
By default replies leave from the Raiseaticket domain. Connecting your Office 365 mailbox means replies are sent from your own address instead, which matters most for customers with strict mail filtering. That is a premium feature.