Re: See also:
The Gateway modules will be 4.5 meters, well withinthe 5.2 meter width of SpaceX's Falcon 9 and Falcon Heavy fairing, and its Power and Propulsion Element (module) must by spec mass less than 7,500 kg. Falcon Heavy can toss at least twice that mass to the Moon.
Since Gateway will be launching in the mid-2020's SpaceX's BFR will also be an option, and it'll be even more capable than SLS of launching massive payloads to the Moon; 45 tonnes for SLS Block 2 (2028+) vs over 100 tonnes for BFR (2020-2022).