Log into your personal Office365 account in your web browser (using the link office365.leeds.ac.uk)

Open Outlook using the icon in the left hand panel, click your profile name in the top right and then click 'open another mailbox'

A box should open prompting you for a mailbox address, enter the address of the shared mailbox you have been given permission to. 

After entering that the mailbox should open in a new tab. In that new tab, click the settings cog and then 'view all Outlook settings'. 

In the settings menu, choose 'automatic replies'

Turn on automatic replies from here and set your message. This shared mailbox will now have an out of office message. If you need to remove an out of office message you would do the same to access this 'automatic replies' section and then untick 'turn on automatic replies'.