I was diagnosed with COPD some 12 months ago, I only gave up smoking just recently and have not smoked for 2 weeks, I have just started coughing up Phlegm with black bits (a bit like pepper bits) !!
This is the bits of tar from the lungs that are repairing themselves a little due to no smoking. However, the lungs will not repair fully as COPD is non reversible unlike Chronic Broncitus etc that can be repaired by not smoking anymore, excersise etc.
The black specs in the Phlegm will continue to show for some months, maybe longer, depending on how long you smoked, I personally smoked cigarettes for 35yrs and weed for approx 25yrs so my personal experience could be longer !!