What an odd situation but, I can see why he might be losing weight.
He starts with carbs during his morning cortisol spike but then keeps insulin very low all day by (almost) fasting and then does not bring up insulin again at dinnertime because he is eating high fat food. Beer - depending on the amount - will bring insulin up a bit and would temporarily stop ketosis (if he was even in ketosis) but, it might also (if consistent) be contributing to a nutrient deficiency (which is a bad form of weight loss).
So, (just my non-doctor opinion) I think he is benefiting from the effects of low insulin (essentially just like intermittent fasting from after breakfast until the next breakfast - OMAD) but, at the same time, I think his breakfasts are keeping him out of ketosis.
Why is it that he might fail and you likely succeed? It is that keto is sustainable - you will be able to stay un-hungry but eat whenever you are hungry and keep losing weight. For him, cereal in the morning and then trying to fast all day can be done for a while by anyone - but eventually the single fruit snack will turn into something more substantial (especially if the beer keeps flowing - morning munchies!) and the required self-discipline will wane (as he is likely not in ketosis with so many grams of carbs daily - so not benefiting from meals to satiety). The low insulin daily period might get smaller and smaller as the non-keto snacks get bigger (or turn into meals) and more spread out. Weight loss will likely plateau/reverse - double down on discipline and - as with most discipline based diets - end in a overall weight gain.
Then, when you talk about keto, maybe he’ll listen!