As you probably know, Earth moon has no appreciable atmosphere.
This is because the combination of its low escape velocity, temperature and lack of magnetic field can allow for just traces of xenon to be kept long enough around it.
Giving a magnetic field to a body like the Moon is difficult: it is small and cools down pretty quickly on cosmic scales, and it also has too little iron to have an appreciable dynamo effect.
If you can't stop the leak, you can still think of pumping more in: an active volcanism might help in releasing more gases in the moon atmosphere, and if the net balance is positive, the atmosphere will grow thicker over time.
However, for volcanism we have the same considerations as for the magnetic field: the little body cools down quickly.
Unless you place it closer to the planet so that the tidal effects keep pumping energy into the planet, heating it up. And also this would not last too long, since the energy put into heating the moon is taken away from the orbiting energy, altering the orbital distance.
Moreover, volcanism alone won't give you a breathable atmosphere, not for humans at least. For that you would need the whole shabang of life and carbon cycle we have on Earth.