Hi @Sam Brewin ,
Should this not allow users from the other tenancy to open and view our calendars? I am under the impression that this org sharing feature allows users to see our calendars without us sending them an invite?
The result of the Org Sharing between two tenants is that users in one organization will be able to view the availability of the other tenant's users when scheduling meetings. See the documentation below for more details:
Organization relationships in Exchange Online
If you need to allow users from the other tenant to open and view the calendar in the calendar list within Outlook, agree with Vasil that it's inevitable for the calendar owner to send a sharing invitation via email.
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