Moving a Plan from an Adhoc Team to an Organizational Team

I think you are mistaking the teams tab as the plan itself. the Tab is just a viewing construct (sort of like a window into something else - in this case a planner plan). Copying/Moving the tab does nothing to the actual plan behind it.

Regarding your situation, a direct move is not possible currently. However you can copy the plan into the new team using the standalone planner app.

Note: You will lose team specific artifacts such as comments and attachments though.