We report Mo isotopic data for 16 15N-rich presolar SiC grains of type AB (14N/15N < solar, AB1) and their correlated Sr and Ba isotope ratios when available. Of the 16 AB1 grains, 8 show s-process Mo isotopic compositions, together with s-process Ba and/or Sr isotopic compositions. We found that a higher percentage of AB1 grains show anomalous isotopic compositions than that of AB2 grains (14N/15N > solar), thus providing further support to the division of the two AB subgroups recently proposed by Liu et al., who showed that AB1 grains most likely originated from Type II supernovae (SNe) with explosive H burning. Comparison of the Sr, Mo, and Ba isotopic compositions of the AB1 grains with SN model predictions indicates that the s-process isotopic compositions of AB1 grains resulted from neutron-capture processes occurring during the progenitor massive stars’ pre-SN evolution rather than from an explosive neutron-capture process. In addition, the observations of (1) explosive H burning occurring in the C-rich regions of the progenitor SNe of X grains as suggested by the isotopic compositions of X grains, and (2) explosive H burning occurring both at the bottom of the He/C zone and at the top of the He/N zone as suggested by model simulations, imply that explosive H burning is a common phenomenon in outer SN zones.