Comets are mostly frozen gasses.
I doubt they would stay frozen after impact.
If a comet hit Earth’s Moon, would an atmosphere form?
And, if so, would it be temporary or permanent?
Yes. Very tempoary. Even a large comet wouldn’t give it more than a very tenuous atmosphere, and the moon doesn’t have enough gravity to hold onto it.
The moon has apparantly been hit by comets repeatedly in the past. There are deep craters at the lunar poles whose bottoms are never touched by sunlight, where there is apparantly ice frozen into the lunar soil, deposited there after comet impacts.
Did you get this idea from my thread asteroid hits moon?
Yes, that & the cometary impact on Jupiter.
The moon does have an atmosphere but it is very thin and IIRC only on the sunlit side of the moon. It’s made mainly of sulfer dioxide.