Some more details:
When event method ON_START is executed i could see that:
contents of context B has data -> its collection_wrapper has entries
The problem is that on the browser in the table where context B data are displayed it is written that object is not bound: "<my_object> not bound"
The other thing i saw is that at this moment: TYPED_CONTEXT->context_B->TABLE is INITIAL,
i.e. there are no data in the variable used by the BSP page to display data.
So i have entries in the BOL collection but they are not displayed on the View.