How did the cork fall into the thermos?
In theory, it's impossible because it's much harder to take it out. I suggest ignoring it and changing the stopper again
Teach you a feasible method to get an airtight plastic bags into the thermos (outside the bag, then left) into the bag wrapped with a mouth blowing, finished, bottle down, pull the plug out of the plastic bag.
Easy way: a hot water bottle, head down, shake the bottle, so that the bottle head down, with the hand can pull out;