Sometimes it’s necessary to let users outside your own organization schedule rooms in your office. Using shared room/resource calendars is an easy way to avoid double bookings. In Exchange, this can be set up in a few steps:
In the admin portal of Organization A: set up an organizational relationship with domain of Organization B.
In the admin portal of Organization B: set up an organizational relationship with domain of Organization A.
Both organizations should now be able to see each others free/busy times as well as available or occupied meeting room times via Outlook. Note: to see the meeting room in Organization A from Organization B, you will have to enter the meeting room email address (e.g. firstname.lastname@example.org).
The problem now is that if someone tries to schedule the meeting room, the room will not process external request. I guess you can see the classic double reservation scenario where people from Organization B think they have booked the room, but people from Organization A have booked it too…
In order for that meeting room to allow external bookings, just run the following via Powershell:
#3 Get-Mailbox "meeting-room-name" | Set-CalendarProcessing -ProcessExternalMeetingMessages $true
Additionally to the above, I added the external email addresses of the rooms as contacts in the external tenant. This allows users to book the rooms from the address book rather than typing the email address of the room manually.
Hope that helps!
https://answers.microsoft.com/en-us/msoffice/forum/msoffice_o365admin-mso_domains-mso_o365b/sharing-meeting-rooms-between-2-office365/c5d6ba4e-678a-49c1-8780-ca39fdb2c0d0?auth=1 (Full post from Microsoft’s community)