Tell your son to start drinking a cup of coffee every other day or so. And it might make his HBSAG go to zero.
I think your son is in a really good place if his HBVDNA or HBSAg staid the same, even if he stopped the pills. Of course I would not have stopped the treatment, he is really close to cure it with such low results. I would definitely follow doctor's advice.
I a not a doctor. In my opinion, your son can stop taking Tenofovir since he is most likely in the Immune Control phase (also known as Chronic Hepatitis B disease phase), because his hbvdna is less than 2,000 iu/ml and his serum HbsAg is less than 1,000 iu/ml. He will still need regular checkups, at least once every twelve months. I also want to tell you that antibodies, such as HBeAb, are made by the human bodies to neutralize the antigens, such as HBeAg, made by viruses and foreign organisms. They are good proteins and are a very important part of our immune system defense against diseases. Your son will be functionally cured when his serum HbsAg disappears (less than 0.05 iu/ml). This may take a long time but not impossible.
No don't continue the medicine. Your son is in remission phase. He may clear hbsag on further cessation of drug. There have been a lot of trials showing positive outcome on stopping nucs after long term therapy. Keep monitoring, and if number deteriorates then start the medicine again. Wait for atleast 76-78 weeks from start.