nostr:npub1eacn5n4e4mj5c06gvqe3l57wf9ss87mq65z83rtuhdu0cy7s5ehqhc5vqz - most things work exactly the same if you stick antiparticles in where you had particles.  So yes: the anti-Higgs boson mediates the mass of antiparticles just like the Higgs mediates the mass of particles.   

BUT: the Higgs boson is its own antiparticle!   In this respect it's like the photon.

As far as we know, the only thing that changes when you replace particles by antiparticles are a few *numbers* describing how *strongly* the Higgs interacts with them.   This makes antimatter behave in a very subtly different way than matter.