Using New Outlook on Windows for personal email, calendar, and contact management
In the new Outlook, if you want to move a folder from a "Shared with me" mailbox to Favorites, be aware that you can make favorites of any of the sub-folders (eg. Inbox, Drafts, Sent Items, etc) but not the whole mailbox.
Start by opening the shared mailbox in the "Shared with me" folder by pressing the > beside the shared mailbox name.
Then right click any of the folders in that shared mailbox and make them favorites.
Alternatively you can drag and drop the folder into Favorites.