"He does not have a phone."
Translation:On nie ma telefonu.
But more common for mobile phone is "komórka", which evolved from "telefon komórkowy"
so "komórka" means "cell" in Polish? in Russian that means a small room with little space
Yes in Polish "komórka" also means small storage room, usually outside of the building, sometimes outside of the apartment.
In english 'cell' also means a jail (which is also a small room - in a police station or a prison).