Additive preservers of mutual strong numerical radius orthogonality

Let $H$ be a complex Hilbert space with $\dim H\ge 2$. We characterize the nonzero additive maps on $\mathcal{B}(H)$ and on its self-adjoint part $\mathcal{B}_s(H)$ that preserve mutual strong numerical-radius orthogonality in one direction, assuming surjectivity only in infinite dimension. These maps are precisely those of the form $A\mapsto cUAU^*$, where $U$ is unitary or antiunitary, and $c$ is a nonzero complex scalar for $\mathcal{B}(H)$ and a nonzero real scalar for $\mathcal{B}_s(H)$.