We show how the static dielectric function and other static characteristics of dense warm charged Fermi liquids can be obtained exclusively from the system static structure factor. The non-perturbative self-consistent method of moments is employed to extend onto quantum fluids, a similar reduction stemming from the fluctuation-dissipation theorem and other exact relations for classical one-component plasmas. The results are compared to and complement the numerical data obtained recently by the path-integral Monte Carlo method. Alternative theoretical approaches are discussed and employed as well.