121.5. If an effect says to “move” a counter, it means to take that counter from the object it’s currently on and put it onto a second object. If the first and second objects are the same object, nothing happens. If the first object has no counters, nothing happens; the second object doesn’t get a counter put on it. If the second object (or any possible second objects) is no longer in the correct zone when the effect would move the counter, nothing happens; a counter isn’t removed from the first object.
It has been previously ruled that Doubling Season will double the counters when counters are moved from one permanent to another, however, 121.5 specifically uses the verb put when it really should use place to be unambiguously consistent with 121.6 and Doubling Season's Oracle text