is there a design pattern who’s structure looks like this. B owns a reference to A, and also do some work using A. and further more, each sub class in hierarchy B relay on a sub class in hierarchy A to do its work.
its code looks like https://codereview.stackexchange.com/questions/12412/two-related-hierarchies-of-classes

This is a parallel inheritance hierarchy, and more commonly viewed as an anti-pattern.
There’s some discussion of it on Ward’s Wiki and at Lambda the Ultimate that might be worth reading.