I am not 100 % sure, but just example from my life. When we had litter at home, our male dog was carrying different things to provide food for nursing mom - from sugarpot on the dining room table to the milking machine from neighbour's barn - all to the nursing bitch. He had not done it before and had not done it after. I presume that it is just instincts telling them to help the nursing bitch. So it really does not mean that he will repeat duck hunting at his new home when separated from litter completely.
Really - now not only sugar pot is left on table, also chocolate is scattered around the house, and no dogs even sniff it, but when the bitch was nursing babies, he was hunting all the time to keep family happy.