The "Move Plans" option from under Administration - > Plans will allow you to move a plan completely to a new or existing project within the same instance of bamboo but it's not a cloning option and you will lose the original plan.
To clone a plan and moving all the logs and histories, there needs to be a partial export/import option and it's not doable at the moment. There is an open improvement request ticket for this feature in our system:
to which you can add yourself as a watcher to recive updates.
When researching for this issue, I also came across the following and thought of sharing them with you in case you want to follow them as well:
Hope this helps!
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