I understood it is a kickoff. If B possessed it at the moment he falls onto it, the ball is dead in his possession. If the ruling is dual possession, dual possession of a kicked ball goes to the receiving team so therefore in either your team B will take possession.
The definition of possession is cited below.
"2-34-ART. 1 . . . A ball in player possession is a live ball held or controlled by a player after it has been handed or snapped to him, or after he has caught or recovered it."
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