  Let $X=\mathbb{P}(\mathcal{O}_{\mathbb{P}^s} \oplus \bigoplus_{i=1}^r
\mathcal{O}_{\mathbb{P}^s}(a_i))$ be a Fano projective bundle over
$\mathbb{P}^s$ and denote by $Crit(X) \subset (\mathbb{C}^{\ast})^n$ the
solution scheme of the Landau-Ginzburg system of equations of $X$. We describe
a map $E : Crit(X) \rightarrow Pic(X)$ whose image $\mathcal{E}= \{E(z) | z \in
Crit(X) \}$ is the full strongly exceptional collection on $X$ found by Costa
and Mir$\acute{\textrm{o}}$-Roig. We further show that $Hom(E(z),E(w))$ for
$z,w \in Crit(X)$ can be described in terms of a monodromy group acting on
$Crit(X)$.
