Mishnah Berurah par. 4 on O.C. 572:1 says that the Chanukah candles should stay lit a minimum of 1/2 hour.
Besides the main mitzvah to light at home, there is a separate one to light in shul, and one makes the blessings in shul (See O.C. 571:7).
A shul davens a late "Ma'ariv" (i.e. a few hours after nightfall) and there was no preceding Mincha service, so they light the menorah as soon as they get a minyan just prior to starting Ma'ariv. The service is quick - less than a half hour in total. For safety reasons, they blow out the candles once Ma'ariv is over (they don't want to leave the building closed with candles burning.)
Since it is known at the beginning, that they won't be leaving the candles lit for the minimum of a half hour, what should they do, halachically?
- Do what they are currently doing, i.e., light, make a bracha and blow out the candles even if under a half hour
- Not light the candles at all
- Light the candles without a bracha