I honestly wouldn't worry about a few things and this is just my opinion as a fighter/trainer:

Don't worry about distance, although roadwork is a vital part of boxing, I feel that because this sport has so many variable energy bursts, training with long paced workouts can only hinder you as a fighter.

The reason I say this is because while you're jogging, you develop a rhythm, you're jogging for an extended peroid of time. How many times in a fight are you at one particular pace for any given amount of time

Basically, when you're fighting, in ANY combative sport, your body is going through quick bursts & moments of rest, and to maintain that cardio during a fight, one must train in that matter.

You say he can do 80 press ups(push ups?) and 80 squats in sets of 10, well why not try explosive intervals of :30 bursts of any work out.

I changed my own work out regiment to follow a strict interval method and after two months, I was able to clock 30rds of sparring weekly, just fine.

Here's an example of a work out I did.

3 minute round
:30 Jump squats as fast as possible
:30 double jump rope as fast as possible
:30 Burpees
:30 Jump slides
:30 jump rope as fast as possible
:30 mountain climbers medium paced

During Rest Period
:30 medium paced jumping jacks
:30 full rest

Repeat x 3

Doing excercises like these, I dropped almost 100lbs and toned my body up better than I have in my entire life.