Hello Eddie,
At this moment you cannot export the content of a Topic, as the scenario you are describing is quite exceptional.
There are a few workarounds though: You can create an identical Topic in the organisation where you need to import the content, and paste the entire thread in this new Topic.
A better alternative for organisations working together on the same project would be to create temporary accounts for the members of one of the organisations in the other one, work together to finalise the project, then suspend these temporary accounts. In this manner, the work would have live input from both teams, rather than just passive info that is read-only.