  The CMS and ATLAS experiments at the LHC have announced the discovery of a
Higgs boson with mass at approximately 125 $GeV/c^{2}$ in the search for the
Standard Model Higgs boson via notably the $\gamma\gamma$ and $ZZ$ to four
leptons final states. Considering the recent results on the Higgs boson
searches from the LHC, we study the lightest scalar Higgs boson $h_{1}$ in the
Next-to-Minimal Supersymmetric Standard Model by restricting the
next-to-lightest scalar Higgs boson $h_{2}$ to be the observed 125 $GeV/c^{2}$
state. We perform a scan over the relevant NMSSM parameter space that is
favoured by low fine-tuning considerations. Moreover, we also take the
experimental constraints from direct searches, $B$-physics observables, relic
density and anomalous magnetic moment of the muon measurements as well as the
theoretical considerations into account in our specific scan. We find that the
signal rate in the two-photon final state for the NMSSM Higgs boson $h_{1}$
with the mass range from approximately 80 $GeV/c^{2}$ to 122 $GeV/c^{2}$ can be
enhanced by a factor up to 3.5, when the Higgs boson $h_{2}$ is required to be
compatible with the excess from latest LHC results. This motivates the
extension of the search at the LHC for the Higgs boson $h_{1}$ in the diphoton
final state down to masses of 80 $GeV/c^{2}$ or lower, in particular with the
upcoming proton-proton collision data to be taken at center-of-mass energies of
13-14 $TeV$.
