  In this paper we study extensions between finite-dimensional simple modules
over classical Lie superalgebras $\mathfrak{gl}(m|n), \mathfrak{osp}(M|2n)$ and
$\mathfrak{q}_m$. We consider a simplified version of the extension graph which
is produced from the $Ext^1$-graph by identifying representations obtained by
parity change and removal of the loops. We give a necessary condition for a
pair of vertices to be connected and show that this condition is sufficient in
most of the cases. This condition implies that the image of a
finite-dimensional simple module under the Duflo-Serganova functor has
indecomposable isotypical components. This yields semisimplicity of
Duflo-Serganova functor for $\mathcal{F}in(\mathfrak{gl}(m|n))$ and for
$\mathcal{F}in(\mathfrak{osp}(M|2n))$.
