Synthesis, X-ray structural, IR and NMR spectroscopic characterization of two new C(=O)NHP(=O)-based phosphoric triamides 2,3,6-F3C8H2C(=O)NHP(=O)[X](2) (X = NC4H8O and NHC(CH3)(3)) are presented. The N-H center dot center dot center dot O(=P/C) hydrogen bonds strengths and stretching frequencies shifts in hydrogen-bonded clusters forming graph-sets R-2(2)(8), R-2(2)(12)/R-2(2)(8) and R-2(2)(10)/R-2(1)(6) in the two new structures and the previously reported structure of 2-FC6H4C(=O)NHP(=O)[NHCH(CH3)(2)](2) are computationally evaluated using the Density Functional Theory (DFT) and the Atoms In Molecules (AIM) theory. It is in particular shown how the strengths of the different N-H center dot center dot center dot O(=P/C) HBs affect the frequencies shifts in hydrogen-bonded clusters. The study is completed by a statistical analysis using data from the Cambridge Structural Database (CSD) and the references that confirm the detailed experimental and theoretical investigations on the two new phosphoric triamides and the analogous compounds.