Additive preservers of mutual strong numerical radius orthogonality

Let H be a complex Hilbert space with H≥2. We show that the additive surjections on B(H) and on its self-adjoint part Bₛ(H) that preserve mutual strong numerical-radius orthogonality in one direction are precisely the maps of the form A↦ cUAU^*, where U is a unitary or antiunitary operator on H and c is a nonzero complex or real scalar, respectively.