Based on your description, he sounds like a
He shouldn't be allowed to pull out his laptop during a flight and get cracking with "other" work either. It's reckless behaviour. This guy has forgotten what he does for a living and should be ashamed of himself.
He's the type of chap that no matter how wrong or inaccurate he might be in something he does or says he can't help but have the last word.
Can't you just ask your crewing team to ensure they DON'T roster him with you for a while. Maybe if other Captains have a similar experience with him and make a similar request to crewing - someone from above might just take this guy to one side and have a quiet word.... ??