  In the present paper, we show a new result on the geometrically $2$-step
solvable Grothendieck conjecture for genus $0$ curves over finitely generated
fields. More precisely, we show that two genus $0$ hyperbolic curves over a
finitely generated field $k$ are isomorphic as $k$-schemes (up to Frobenius
twists) if and only if the geometrically maximal $2$-step solvable quotients of
their \'etale fundamental groups are isomorphic as topological groups over the
absolute Galois group of $k$.
