This isn’t obvious as it’s not possible to do within the desktop Outlook client for a shared mailbox, the option just isn’t there for managing any shared mailbox that your Outlook client automatically adds.
To work around this, it’s possible to set an Automatic Reply within webmail for the shared mailbox.
Firstly, logon to Office 365 webmail using your email address and password. Once logged in, depending on your level of access you will either go direct to the Outlook web client or the Office 365 portal – either way, you need to go to the Outlook web client. You can select this by clicking on the top left hand Menu icon (3 x 3 square of white dots) and selecting Mail.
Once you’re logged in to your mailbox in Outlook web client, click on your name in the top right hand corner and select ‘Open another mailbox…’:
In the new pop up window, start typing the address of the shared mailbox until it’s available in the drop down box then select it from there:
Then select ‘Open’ and a new tab should appear with the shared mailbox open in the Outlook web client.
Click on the cog icon in the top right hand corner then select ‘Automatic Replies’:
Here, you can set your automatic reply options for a period time and different messages for internal and external senders.