Does swallowing food stuck in the throat after suhoor or swallowing the moisture remaining in the mouth from water drunk before the Fajr athan break one's fast?

It is unlikely for food to remain lodged in the throat for a long time, and what the questioner feels might be mere waswasah (whispers from Satan). In any case, if food descends into the throat before the fast and does not return to the mouth, then swallowing it from the throat during the fasting period does not invalidate the fast, even if done intentionally. Similarly, if nothing remains of water in the mouth except its moisture along with saliva, then swallowing the saliva at that point does not invalidate the fast.