  In this paper, we present some sufficient conditions on a metric space $M$
for which every elementary molecule is a strongly subdifferentiable (SSD, for
short) point in the Lipschitz-free space $\mathcal{F}(M)$ over $M$. Our main
result reads as follows: if $(M,d)$ is a metric space and $\gamma > 0$, then
there exists a metric $d_{\gamma}$ in $M$ such that every finitely supported
element in $\mathcal{F}(M, d_{\gamma})$ is an SSD point. Consequently, the
subset of all SSD points in $\mathcal{F}(M, d_{\gamma})$ is dense.
