Good news, this feature is partially done. :)
Planner tasks can now be copied to other plans. To copy a task, click on the “…” menu on the task. From there, you can select a different plan to copy the task to.
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Once a Planner board has been created for a channel, it sems to be impossible to move it between teams.
A workaround is to create the new board in the new team, open Planner via the Office Hub (where you would see ALL your boards) and COPY tasks one by one from the previous board into the new one (right-click on task).
However, copying does NOT include comments and attachments ...