Continuous coexistency preservers on effect algebras

Let $H$ be a finite-dimensional Hilbert space, $\dim H\ge 2$. We prove that every continuous coexistency preserving map on the effect algebra $E(H)$ is either a standard automorphism of $E(H)$, or a standard automorphism of $E(H)$ composed with the orthocomplementation. We present examples showing the optimality of the result.