How to define a Function in a submesh based on function values present in an adjoining submesh?

Hi, Please add a minimal working code example, as described in Read before posting: How do I get my question answered?
Without such an example, it requires more effort from the community to try to help you with your problem, as one has to create example code and hopefully interpret your question correctly. Especially since SubMesh is a relatively new feature, a code example will help others that might face similar problems.