Absolute universality conjecture for the natural embedding of the Lie incidence geometry

Let $\mathbb{F}$ be a field, let $A_{n,\{1,n\}}(\mathbb{F})$ be the Lie incidence geometry, and let $\varepsilon_{\mathrm{nat}}$ denote its natural embedding. An embedding is absolutely universal when every projective embedding of the geometry is obtained from it by projection. Absolute universality conjecture. If

$$|\operatorname{Aut}(\mathbb{F})|=1,$$

then $\varepsilon_{\mathrm{nat}}$ is absolutely universal. The conjecture is motivated by the fact that when $|\operatorname{Aut}(\mathbb{F})|>1$, the geometry admits no absolutely universal embedding, while the claim is known when $\mathbb{F}$ is a prime field and $n>2$.