Additive preservers of mutual strong numerical radius orthogonality

Let $H$ be a complex Hilbert space with $\dim H\ge2$. We show that the additive surjections on $\mathcal{B}(H)$ and on its self-adjoint part $\mathcal{B}_s(H)$ that preserve mutual strong numerical-radius orthogonality in one direction are precisely the maps of the form $A\mapsto cUAU^*$, where $U$ is a unitary or antiunitary operator on $H$ and $c$ is a nonzero complex or real scalar, respectively.