I answered this on the https://boardgamegeek.com/thread/1625448/parting-gifts-beorn
thread. Short version: it won't work, because "Immune to player card effects" covers the card
, not the hero. So whether or not you're right in claiming that Beorn's resource pool is a separate concept from Beorn, it doesn't matter. Because the resource pool is certainly part of the card
, and thus "Immune to player card effects" forbids you from influencing it with Parting Gifts.