Create a Mail Flow Rule (Transport Rule) in Exchange Admin Center

Best if you're an M365 admin and want a reliable, server-side rule that applies even if no one's signed into the shared inbox.

Go to the Microsoft 365 Admin Center → Expand Admin centers → Open Exchange.
In the Exchange admin center, go to Mail flow → Rules.
Click Add a rule (+) and select Create a new rule.
Name the rule something like: Block emails to software.firmware.updates@kingsltd.co.uk from @kingsltd.co.uk.
Under Apply this rule if...:
- Select The recipient is... → choose software.firmware.updates@kingsltd.co.uk
- Click Add condition and select The sender domain is... → enter kingsltd.co.uk
Under Do the following:
- Choose either Delete the message without notifying anyone or Reject the message with explanation, depending on your preference.
Click Next, then Finish and Save the rule.

This rule will silently block emails from @kingsltd.co.uk going to that shared inbox.