Hi folks.
The quickest way I found so far:
1 - Double click on the face that you want to keep to select it and its perimeter.
2 - Make a group with the selection.
3 - Triple click the other face to select it, its perimeter and all the other edges and faces that make the sides of the thick wall.
4 - Delete the selection. Only the group will remain.
5 - Explode the group, if needed.
In step 1, if you single click the face, you will need to use the Edit Menu --> Make group to create the group since the contextual menu don't show the choices to create a group or a component when a single entity is selected. This glitch has already been reported to the developers of SU. I know it makes ne sense to consider grouping only one entity since it is, after all, alone, but, to separate it from other geometries, it makes sense.
See this SU file for ideas: