How to set/update an automatic reply for a shared mailbox
You want to set or update the automatic reply message on a shared mailbox. This can be done in either Outlook for the web or the desktop Outlook app.
Outlook for the Web
Sign in at https://outlook.office.com/mail/ as your own account
Click on your picture or initials in the upper right corner and select the “Open another mailbox …” option
In the search input area, enter the email address of the shared mailbox as the email (it will likely self-complete as you type)
That should open the shared email account in a new window
In the upper-right, click on the settings gear icon and select Account option
You should see Automatic replies listed there as an option and be able to edit the text of the current message (or turn on/off).
Outlook Desktop app
Reference: How to Set up automatic replies for Shared Mailbox - o365info
You need to go to the File tab in Outlook
Select the shared mailbox from the dropdown list of of accounts at the top
Then you should be able to set and edit the Automatic Replies in that Account Information pane for the selected account