  The semileptonic decay $D^{+}_{s}\rightarrow \pi^{+}\ell^{-}\ell^{+}$, where
$\ell=e, \ \mu$, is used as a reference channel when looking for suppressed or
forbidden processes of the standard model of the form $D_{s}\rightarrow
P\ell^{\pm}\ell^{\prime+}$. The process is dominated by hadronic resonances
from the $\eta$ to the $\phi$ meson region, usually excluded due to the large
uncertainties associated. In this work, we explore the role of the parameters
involved in the resonance region. We focus in the relative strong phase between
the $\rho$ and the $\phi$ meson ($\delta_{\rho\phi}$). We argue that this
parameter can be bound from LHCb data of the di-muon invariant mass in the
$D^{+}_{s}\rightarrow \pi^{+}\mu^{-}\mu^{+}$ decay and we perform a fit to
provide a first approach to it. We obtain $\delta_{\rho\phi}=(0.44 \pm 0.24)
\pi$. In contradistinction, it would be useful to consider observables
insensitive to this phase. We first compute the invariant mass of the lepton
pair at a given angle of one of the leptons emission with respect to the pion,
and then we compute the forward-backward distribution at such angle. We show
that for the latter observable the resonance region is smeared, exhibiting no
dependence on the $\delta_{\rho\phi}$ phase, although global effects are
observed by comparing with the pure phase space approach. In order to consider
this observable in more general scenarios, we analyse the behavior for the
resonant background process $D^{+}_{s}\rightarrow \pi\pi\pi$, the short
distance contribution in the standard model, and the charged Higgs mediated
process as given by the two Higgs doublet model, which exhibit distinguishable
features among themselves.
