Shared iOS calendar events do not automatically appear in Outlook unless those events belong to an account that is synced to Outlook. Events added only to the iPhone calendar need to be added through a synced account such as iCloud, and that account must then be added to Outlook.
If the goal is to see Outlook/Exchange calendar data on the iPhone, check these items:
- On the iPhone, open Settings > Apps > Calendar > Calendar Accounts.
- Select the Outlook/Exchange account and make sure Calendar is turned on.
- Open the iPhone Calendar app, tap Calendars, and confirm the Outlook calendar is selected.
- If the account was added as IMAP, remove it and add it again as Exchange or Outlook.com. IMAP and POP sync email only, not calendar or contacts.
If the issue is specifically that events created by a family member in a shared iPhone calendar are not showing in Outlook, the supported behavior is that device calendar events show in Outlook only when they are added through an account synced to Outlook. A shared local iPhone calendar is not described as syncing directly into Outlook.