The SLS delivered a crew capable Space Vehicle to Lunar orbit, and the space vehicle returned a crew capable capsule back the Earth. The lift capacity of FH is not capable of that. This is all about SWaP: Size, Weight, and Power.

The idea that all the components have to go up on a single launcher is nonsense used to justify SLS. It's political engineering, not rational mission design.

I don't think a Falcon Heavy would retain enough fuel once getting itself in orbit with 0 payload to give enough delta-V to the entire Artemis Space vehicle. That burn has to (generally) happen in a single TLI burn. So there is actually a minimum quanta of delta-V for the mission I don't think FH could meet. You're welcome to run this in Orbital STK if you like.

Propellant transfer. There's a reason Senator Shelby was so adamant NASA not work on it -- it greatly reduces any need for a launch vehicle as large as SLS.

Specifically it completely eliminates the need for a non-reusable launch vehicle as large as SLS.

Granted that this is true, FH right now does not have these capabilities and SLS has already done it. For all the amazing success of FH it's completely the wrong vehicle for a mission like this, which is why Starship exists and IMHO is the future.

The point is the mission was designed to prop up SLS, not designed to actually be worth doing. A base on the moon could be supported with FH, and much more cheaply than one supported by SLS.