That's reeeeeally normal after an upper respiratory infection, and will go on for months if he had pneumonia. It takes awhile to get the phlegm all moved out.
Honestly, if he's not regressing (exercise shuts your immune system down while you're exercising... hence why moms are sick forever, we keep shutting our immune systems down and the infection gets a toehold... 2 steps forward, 1 step back... why kids and husbands who get to sleep and be taken care of get well quite quickly. Of course, I'm generalizing, I'm sure many husbands take time off work to take care of their sick wives so they can sleep and get better, I just don't know any... and I know many parents who drag their sick children around instead of letting them rest and they stay sick for ages longer than they would if they weren't)...
Anyhow... exercise when you're STARTING to get better, can cause a full on relapse... but if he's BETTER, just still moving the phlegm out; Have at!