hello and welcome to HCM,
Since you mentioned that he has undergone adenoid
operation then it is understood that he underwent the same because he had nose block and recurrent infection.
Since he would have had nose block for many years, he would have naturally being breathing through the mouth. Now even if his nose block is gone or disappeared, he still may breath through the mouth because of habit.
In the first part of his treatment you need to get a complete ENT assessment including if possible endoscopy
to confirm that he has no nose block at present.
Once it is confirmed that he has no nose block then you must vigorously instruct him to breathe only through the nose and not through the mouth.
This should be followed strictly throughout the day with someone strictly pointing out to close his mouth and breath only through the nose. This cannot be much forced when he is sleeping though but when he consciously starts breathing through the nose in the daytime or when he is awake, his body will tune itself to do so when he is asleep.
Also do steam inhalation especially in the night to help him in his breathing
Needless to say that if he has any nose block at present that should be first corrected
Dr Sriram Nathan