Two related issues:
(1) "Copy Class" and "Move Class" can't be invoked on a nested class.
(2) "Copy Class" and "Move Class" can't copy/move into a nested class scope.
One common use case is cloning a nested class, for which you'd need both (1) and (2).
Copy and Move refactoring are implemented for java files not classes for now.
It is possible to use Move Inner To Outer + Move refactorings as a work around for Move Nested.
For the most interesting use cases there is no workaround as there is no "Move Outer To Inner".