In this paper we consider a family of projective embeddings of the geometry $Γ= A_{n,\{1,n\}}(F)$ of point-hyperplanes flags of the projective geometry $Σ= PG(n,F)$. The natural embedding $\varepsilon_{mathrm{nat}}$ is one of them. It maps every point-hyperplane flag $(p,H)$ of $Σ$ onto the vector-line $\langle x\otimesξ\rangle$, where $x$ is a representative vector of $p$ and $ξ$ 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 $σ\in Aut(F)\setminus\{\mathrm{id}_F\}$, the twisting $\varepsilon_σ$ of $\varepsilon_{\mathrm{nat}}$ by $σ$ maps $(p,H)$ onto $\langle xσ\otimes ξ\rangle$. We shall prove that, when $|Aut(F)| > 1$ a geometric hyperplane $\cal H$ of $Γ$ arises from $\varepsilon_{\mathrm{nat}}$ and one of its twistings or from two distinct twistings of $\varepsilon_{\mathrm{nat}}$ if and only if ${\cal H} = \{(p,H)\in Γ\mid p\in A \mbox{ or } a \in H\}$ for a possibly non-incident point-hyperplane pair $(a,A)$ of $Σ$. We call these hyperplanes quasi-singular hyperplanes. With the help of this result we shall prove that if $|Aut(F)| > 1$ then $Γ$ admits no absolutely universal embedding.