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To publish a calendar as a .ics, you will first need owner rights to the calendar. If it's your own calendar, you automatically have owner rights on it. For shared calendar mailboxes, you get this by being a member. Then, you need to open the shared mailbox in the Outlook Web App in your browser (outlook.office.com). You can open it using the Open another mailbox dialogue in the top right of your screen, where your profile picture/account initials are.
Open the account you are planning to share the calendar of via email or display name, then open the settings cog.
Go to Calendar > Shared calendars > Publish a calendar and select the calendar you wish to share as well as the permissions level you want others to have, then Publish. The ICS link provided gives those that add it to their calendar view an automatically updating calendar with the data you've shared.
