To tell them to stop coughing?

[crappyday2018]

I've just moved into a new place (rented) for a while until i can buy again. Its a maisonette so I have neighbours either side and below but its actually lovely and quiet. I was pleasantly surprised.
However, the old man next door has carers in 24/7 (and his daughter lives there too I think). The carer who always seems to do the night shift smokes like a chimney. He stands in the back yard at all hours of the night coughing his lungs up. Its that proper smokers hacking cough. It wakes me up every single night.
AIBU to open the window and tell him to shut up? If it was the actual neighbour I might be more polite about it, but its driving me insane.

Would his employer (care agency etc) be happy about him smoking at work?

Speak to your letting agent, see if they will contact the neighbour or the care agency.

I don’t think ywbu to shout out of the window. It would be kinder than writing to the care company he works for. It’s inconsiderate of him to make a noise in the middle of the night.

Thanks all. I'm not sure if I'd feel comfortable complaining to his employer because the family might be pi**ed off at me doing that. They clearly have no issue with him standing smoking outside (they also smoke). It would be obvious it was me who complained as I've just moved in.
I thought if I said something direct to him when he;s doing it then it give him the chance to stop before I took it further.
I hate the thought of 'shouting out the window' but at least I've tried that before complaining.