Sorry, looking at get the latest fragment in backstack I understood that findFragmentByTag(tag) finds the last fragment with required tag. In my case after adding many fragments it sometimes found not last fragment with tag, but a previous to last (with the same tag). Maybe there is a bug in my code, I don't know, why is that.
First I tried to use callbacks, then tried to use parentFragment and childFragmentManager, see getParentFragment returning null. In fragment D I called parentFragment and accessed to methods of A and could update the last A fragment. This solution has two problems.
1) Child fragment (D) inherits a toolbar from parent (A) and adds own buttons. And after clicking Back button we return not to a parent, but even quit parent (A).
2) If we want to update not previous fragment (so that between A and D are also 3 fragments), it seems to be impossible.
So, I cancelled that solution and changed the application behaviour. I clear a backstack where it is possible. So that we cannot have two A fragments in backstack. I use supportFragmentManager.popBackStack(null, FragmentManager.POP_BACK_STACK_INCLUSIVE). Yes, that's a workaround, but I don't know, how to deal with that bug.