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I can only find figures for the Expendable configuration - 63.8 metric tons. The Wikipedia article says

The partially reusable Falcon Heavy falls into the heavy-lift range of launch systems, capable of lifting 20 to 50 metric tons into low Earth orbit (LEO), under the classification system used by a NASA human spaceflight review panel. A fully expendable Falcon Heavy may also reach the super heavy-lift category (above 50 metric tons to LEO).

However, this ballpark range has no reference other than a NASA report that makes no mention of Falcon Heavy and is only used to define rocket categories (heavy-lift and super heavy-lift).

Now, I did find this quote on Teslarati, of all places, but it isn't referenced, and as sites that specialize in this area have not named a figure, I'm not sure of its accuracy

...the fully reusable Falcon Heavy has a max payload of about 23,000 kg to LEO and 8,000 kg to GTO.

I do note that the Wikipedia article does have a figure of 8000 kg to GTO, from which the other orbits could be extrapolated, but that gets a different figure than the one mentioned above and is perhaps a bit simplistic. Using Spacex's published payload capacities, that implies 19 tons to LEO.

So how much can the FH Reusable lift?

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  • $\begingroup$ Small bit: according to Elon Musk's Twitter feed, center core expended side cores recovered (on drone ships) is a 10% hit on capacity over full expendable configuration, which would imply ~56 tons to LEO. I suspect due to the tyranny of the rocket equation the hit is worse for higher energy orbits, but I haven't done the math. $\endgroup$ – ORcoder Feb 17 '18 at 21:24
  • $\begingroup$ Source for the 10% hit: mobile.twitter.com/elonmusk/status/963094533830426624 $\endgroup$ – ORcoder Feb 17 '18 at 22:06
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According to SpaceX web-site, the Falcon Heavy has the following max capacities (presumably fully expended).

Fully Expended Capacities

  • LEO: 63,800kg
  • MARS: 16,800kg
  • GTO: 26,700kg
  • PLUTO: 3,500kg

Based on Elon's tweet from @ORCoder, if you drone ship land the side-cores and just expend the center core you only lose 10%.

Core Expendable Only Payloads

  • LEO: 57,400kg
  • MARS: 15,000kg
  • GTO: 24,000kg
  • PLUTO: 3,150kg

Now for fully re-usable, we have this article from Aviation Week where Elon is talking about GTO payloads.

"Falcon Heavy will do satellites up to 7 tonnes with full reusability of the all three boost stages,” he said, referring to the three Falcon 9 booster cores that will comprise the Falcon Heavy's first stage. He also said Falcon Heavy could double its payload performance to GTO “if, for example, we went expendable on the center core."

But Elon said this in 2014 before they made substantial improvements to their launch stacks, including chilling propellants to increase density. The FH wikipedia entry says that claimed FH max payloads have increased roughly 20% since then giving an expendable GTO payload of 7,600kg, which seems really low. But he also says it's half of the core expendable GTO, which would be 12,000kg, so he contradicts himself. So using these values as a range and extrapolating to the other payloads using the fully expendable relative proportions we get.

Fully Reusable Payloads

  • LEO: 18,000 - 28,400kg
  • MARS: 5,000 - 7,900kg
  • GTO: 7,600 - 12,000kg
  • PLUTO: 1,000 - 1,600kg
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