Assuming I have a instance of class A (name it AI)
that has an instance of class B (name it BI).
Can a reference to BI (somewhere else) tell me that it is part of AI?
I don't talk about inheritance/parent class.
I know I can do this by implementing a reference to A
in the constructor of B - but can mighty Python do it for me?
can mighty Python do it for me?

No, you have to do it yourself (by having every instance of B keep a reference to the corresponding instance of A).
Get containing python class from element