  In this paper we consider a family of projective embeddings of the geometry
$\Gamma = A_{n,\{1,n\}}(F)$ of point-hyperplanes flags of the projective
geometry $\Sigma = PG(n,F)$. The natural embedding $\varepsilon_{mathrm{nat}}$
is one of them. It maps every point-hyperplane flag $(p,H)$ of $\Sigma$ onto
the vector-line $\langle x\otimes\xi\rangle$, where $x$ is a representative
vector of $p$ and $\xi$ is a linear functional describing $H$. The other
embeddings have been discovered by Thas and Van Maldeghem (2000) for the case
$n = 2$ and later generalized to any $n$ by De Schepper, Schillewaert and Van
Maldeghem (2023). They are obtained as twistings of
$\varepsilon_{\mathrm{nat}}$ by non-trivial automorphisms of $F$. Explicitly,
for $\sigma\in Aut(F)\setminus\{\mathrm{id}_F\}$, the twisting
$\varepsilon_\sigma$ of $\varepsilon_{\mathrm{nat}}$ by $\sigma$ maps $(p,H)$
onto $\langle x\sigma\otimes \xi\rangle$. We shall prove that, when $|Aut(F)| >
1$ a geometric hyperplane $\cal H$ of $\Gamma$ arises from
$\varepsilon_{\mathrm{nat}}$ and one of its twistings or from two distinct
twistings of $\varepsilon_{\mathrm{nat}}$ if and only if ${\cal H} = \{(p,H)\in
\Gamma \mid p\in A \mbox{ or } a \in H\}$ for a possibly non-incident
point-hyperplane pair $(a,A)$ of $\Sigma$. We call these hyperplanes
quasi-singular hyperplanes. With the help of this result we shall prove that if
$|Aut(F)| > 1$ then $\Gamma$ admits no absolutely universal embedding.
