Strong block universality of Conway's Game of Life

Let $g:\{0,1\}^{\mathbb Z^2}\to\{0,1\}^{\mathbb Z^2}$ be Conway's Game of Life map. Does $g$ strongly simulate every block map $\phi:Y\to D^{\mathbb Z^2}$ whose domain $Y$ is a two-dimensional subshift of finite type? Explicitly, for every such $\phi$, do there exist positive integers $m,n$, an injective macrotile substitution $\tau:D\to\{0,1\}^{[m]\times[n]}$, and a bijective partial block map $h$ from the Life configurations $x$ satisfying $g(x)\in\tau(D^{\mathbb Z^2})$ onto $Y$, such that $g(x)=\tau(\phi(h(x)))$ for every such $x$?