You cannot do this directly, as the cyclic expression group you created only exists locally within the object and remains unnamed. Dimension (Cyclic/Drill-Down) groups OTOH are created globally and are linked anyway, but not so with these expression groups.
There is however an interesting workaround you can use to simulate what you want, without containers, without buttons etc. and without any apparent difference with the ideavyou had in mind.
See How to get the used expression? by the one-and-only JohnW
