Look at their chest........I wish I could link a grade A post from my boy Yuzo about this. You can tell from your opponents chest and back shoulder what punch they're going to throw. But the answer is to fight off the front foot pivot. To do this, first shift your body weight over your knee. You'll notice from here you are A) closer to your opponent B) your body is lower C) your power is loaded up like you're about to throw a left hook. From this position you are 'in the pocket'. Here you should be able to reach your opponent with any type of jab that you throw, while also being able to escape by pushing down and backwards on your front foot. This allows you to stay in position to get your punches off, and having a good escape route.
The best way is to get off first be close and pressure him while patient until you can land 2/3 shots in succession to make him think..( most counter punchers will only look for one punch to counter), really the only way to fight a defensive counter puncher and not let him dictate space and distance to time his counter shots. Throwing body to head combos is a good way to disrupt his rhythm ....but impossible to say exactly without footage or dimensions of both guys. If you find it diificult to get the jump on him ,hit his gloves stepping back and forth,make him reset,because a counter puncher relies more on timing.
Also lateral movement disrupts a counter punch a lot. But what disrupts a counter puncher more than anything is creating a counter to the counter. For example many orthodox punchers counter a jab by going over the top with a right hand. If you know your opp is going to do this, you could throw a short jab and pivot into a check hook over the top of their shoulder.
Hes fighting a defensive counter puncher whos just leaning back while back peddling making him miss and unloading a big shot I think? this type of fighter is not so easily counter/countered. because hes not engaging the fight hes being passive/aggressive...best way is to disrupt distance slowly ,then get in head/body combos ,even getting out and resetting yourself until you either make him off timed or you yourself create the moment to be aggressive...idk? its difficult without footage...lol im assuming hes also shorter because hes having trouble closing distance. you really just have to off set the guy with the above,mainly footwork until in position and get under him hit in flurries if that's what needs to be done, again I cant really give solid advice without footage on this one. chasing down a guy who waits from a distance with long reach is never fun, from experience me countering this type of guy almost never worked ,I had to engage and disrupt giving to much reach. it actually sounds just like he lacks experience to a guy who knows how to avoid hits.