  For a toric Fano manifold $X$ denote by $Crit(X) \subset
(\mathbb{C}^{\ast})^n$ the solution scheme of the Landau-Ginzburg system of
equations of $X$. Examples of toric Fano manifolds with $rk(Pic(X)) \leq 3$
which admit full strongly exceptional collections of line bundles were recently
found by various authors. For these examples we construct a map $E : Crit(X)
\rightarrow Pic(X)$ whose image $\mathcal{E}=\left \{ E(z) \vert z \in Crit(X)
\right \}$ is a full strongly exceptional collection satisfying the M-aligned
property. That is, under this map, the groups $Hom(E(z),E(w))$ for $z,w \in
Crit(X)$ are naturally related to the structure of the monodromy group acting
on $Crit(X)$.
