если это новость ,present perfect

странно,что никто не предложил самый частый вариант через give up

Как скажете 😄

Gave up smoking vs quit smoking: https://books.google.com/ngrams/graph?content=gave+up+smoking%2C+quit+smoking&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cgave%20up%20smoking%3B%2Cc0%3B.t1%3B%2Cquit%20smoking%3B%2Cc0

Alex, QUITTED is incorrect. The past tense is QUIT

Valery, (1) there’s no call for the past perfect here; and (2) kick the habit means to finally quit something after trying many times.

Tatiana is right - if this is an announcement, then the present perfect. If it’s just a fact, then the simple past: “The boss is in a terrible mood today - she’s quit smoking again.” -or- “Ever since her sister died, Eva has tried to lead a healthy life - she changed her diet, quit smoking and is jogging.”