The Hubble Space Telescope WFPC2 camera has been used to image Andromeda?II, a dwarf spheroidal (dSph) companion to M31. The resulting color-magnitude (c-m) diagrams reveal the morphology of the horizontal branch (HB) in this dwarf galaxy. We find that like Andromeda?I, and like most of the Galactic dSph companions, the HB morphology of And?II is predominantly red. Unlike And?I, however, there is no evidence for a radial gradient in HB morphology in the And?II data. Based on a comparison with a combination of standard Galactic globular cluster c-m diagrams scaled to reproduce the And?II mean abundance and abundance dispersion, we interpret the observed HB morphology of And?II as indicating that at least 50% of the total stellar population is younger than the age of the globular clusters. This inference is strengthened by the small number of confirmed upper-AGB carbon stars in And?II. The relatively faint luminosities (Mbol ? -4.1) of these stars, however, suggest an age or ages nearer 6?9 Gyr, rather than 1?3 Gyr, for this population. On the other hand, the existence of blue HB and RR?Lyrae variable stars in And?II argues for the existence of an additional old (age > 10 Gyr) population in this dSph. Thus, And?II has had an extended epoch of star formation like many of the Galactic dSphs. The mean magnitude of the blue HB in And?II suggests (m-M)0 = 24.17 ? 0.06 and that And?II is 125 ? 60 kpc closer than M31 along the line of sight. This confirms the association of And?II with M31, rather than with M33 to which And?II lies closer on the sky. The true distance of And?II from the center of M31 is between ~160 and ~230 kpc, comparable to the Galactocentric distances of Fornax and of the Leo dSphs. With the current samples of dSph companions, the size of the Galaxy's and M31's dSph satellite systems are comparable, with outer radii of order 250 kpc. The And?II red giant branch colors yield a mean abundance of [Fe/H] = -1.49 ? 0.11 and a surprisingly large internal abundance spread, which can be characterised by ?int([Fe/H]) ? 0.36 dex. Both these values are in good agreement with the recent ground-based spectroscopic study of C?t? et al. The And?II abundance dispersion found here is considerably larger than that derived for And?I from an identical analysis of similar data (?int([Fe/H]) = 0.21 dex). Thus, despite having very similar luminosities and mean metal abundances, these two M31 dSph companions have clearly had different chemical evolution histories. We find that we cannot model the abundance distribution in And?II with single component simple chemical enrichment models. However, we can reproduce the form of the distribution if we assume two components, each with a simple model abundance distribution. The metal-poor component has mean abundance log(z/zsun) = -1.6, while the metal-rich one has mean abundance log(z/zsun) = -0.95 and is outnumbered by the metal-poor population by a ratio of ~2.3 to 1. We end by concluding that the diversity of evolutionary histories evident among the Galactic dSph companions is now also firmly established among the dSph satellites of M31. An Appendix discusses minor revisions to our earlier And?I results that arise from the calibration and analysis techniques adopted in this paper. In particular, our comparisons with ground-based photometry indicate that the zero point for the WFPC2 F450W to B transformation should be modified, by 0.055 mag, to produce fainter B magnitudes and thus redder B-V colors.