Hi Pamela,
I am not sure exactly what you are wanting to accomplish, but you should be able to drag the test from the current test set into the desired new test set. You could also copy the test and place a copy in the newly desired test set location. IS it that you can not accomplish this, then further clarification would be needed, as it may be that you have customized settings that are not allowing the permissions to accomplish this.

Let us know further if this does not work for you or there is something more that you are requiring.

Thanks,
Dan

Experimenting with ALM v11 patch 12 I found...

You cannot drag and drop a test instance in a test set to another test set.

If you copy a test set, it will no copy existing results.

You can drag and drop a test set from one test folder to another, and that WILL bring the results with it.