Cross-correlations techniques offer an alternative method to search for molecular species in James Webb Space Telescope (JWST) observations of exoplanet atmospheres. In a previous article, we applied cross-correlation functions for the first time to JWST NIRSpec/G395H observations of exoplanet atmospheres, resulting in a detection of CO in the transmission spectrum of WASP-39b and a tentative detection of CO isotopologues. Here, we present an improved version of our cross-correlation technique and an investigation into how efficient the technique is when searching for other molecules in JWST NIRSpec/G395H data. Our search results in the detection of more molecules via cross-correlations in the atmosphere of WASP-39b, including $\rm H_{2}O$ and $\rm CO_{2}$, and confirms the CO detection. This result proves that cross-correlations are a robust and computationally cheap alternative method to search for molecular species in transmission spectra observed with JWST. We also searched for other molecules ($\rm CH_{4}$, $\rm NH_{3}$, $\rm SO_{2}$, $\rm N_{2}O$, $\rm H_{2}S$, $\rm PH_{3}$, $\rm O_{3}$, and $\rm C_{2}H_{2}$) that were not detected, for which we provide the definition of their cross-correlation baselines for future searches of those molecules in other targets. We find that that the cross-correlation search of each molecule is more efficient over limited wavelength regions of the spectrum, where the signal for that molecule dominates over other molecules, than over broad wavelength ranges. In general, we also find that Gaussian normalization is the most efficient normalization mode for the generation of the molecular templates.