Saturn V could lift 140 tonnes to low earth orbit. Falcon Heavy can lift 54 tonnes to low earth orbit. I think that means it could get a mission to the moon as long as it weighed 38% of what Apollo did. That doesn't sound like a fun trip.
Unless you assemble the moon ship in earth orbit first. Falcon Heavy can launch Orion on its own, or the European Service Module that it requires. I imagine it could launch a lunar lander too. You would also need a booster to send the combination to the moon - the Saturn final stage that did that weighed 100 tonnes, twice what Falcon Heavy can launch. So, maybe you launch an empty booster, and send up a couple of tankers to fuel it on orbit? It's a lot of launches, and a lot of work to do in orbit. That's not impossible (and is cool as hell), but there would be a lot of work to do to make it possible.