It is not uncommon for a person to develop a productive cough following smoking cessation, as one’s lungs recover and the bronchial tubes are able to clear accumulated “crap” out of the lungs.
This can occur just about anytime following smoking cessation and may continue for 6-12 months. That may be what is happening.
On the other hand, what you describe may be a sign of infection and may be accompanied by fever, fatigue, malaise and/or loss of appetite. I suggest that you contact your doctor for further advice and, if deemed appropriate by him/her, antibiotic therapy.
Good luck
I am not an MD and don't play one on TV.
afaik, white/ pale green phlegm is somewhat normal for COPD.
Green means maybe an infection - - see you doctor soon.
Brown means you inhaled a small animal - see MD ASAP.
Best of luck.