It would not be possible to completely move the test and maintain the history. The way you could accomplish this though would be to create a version of your original test, call say old version. This will allow users to know this is the old test.
You can then Copy the Test and Past this to the other Test Container, this will create a new version of this test in the new location.
You could then add an attribute or a way of allowing users to see this linked to old test case.
Any issues let us know.