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Hi Carmie,
You can invite users outside of your organisation to join a specific group. Just as you would invite users within your organisation but untick the box that says "Only search for members in your organisation".
Their profile will need to be public for you to be able to search for them: under my profile it needs to say Who can see your profile? Everyone (public)
As I understand it, the admin or Org B will then be able to view all the contents within the group of Org A, and contribute as a normal user.
We use this method for exactly the same reason you suggest. Inviting stakeholders to view a specific subset of our data.
Hope this helps,
Andy