We derive dust masses (M dust ) from the spectral energy distributions of 58 post-starburst galaxies (PSBs). There is an anticorrelation between specific dust mass (M dust /M ) and the time elapsed since the starburst ended, indicating that dust was either destroyed, expelled, or rendered undetectable over the ∼1 Gyr after the burst. The M dust /M depletion timescale, 205 +58 −37 Myr, is consistent with that of the CO-traced M H2 /M , suggesting that dust and gas are altered via the same process. Extrapolating these trends leads to the M dust /M and M H2 /M values of early-type galaxies (ETGs) within 1-2 Gyr, a timescale consistent with the evolution of other PSB properties into ETGs. Comparing M dust and M H2 for PSBs yields a calibration, log M H2 = 0.45 log M dust + 6.02, that allows us to place 33 PSBs on the Kennicutt-Schmidt (KS) plane, ΣSFR − ΣM H2 . Over the first ∼200-300 Myr, the PSBs evolve down and off of the KS relation, as their star formation rate (SFR) decreases more rapidly than M H2 . Afterwards, M H2 continues to decline whereas the SFR levels off. These trends suggest that the star-formation efficiency bottoms out at 10 −11 yr −1 and will rise to ETG levels within 0.5-1.1 Gyr afterwards. The SFR decline after the burst is likely due to the absence of gas denser than the CO-traced H 2 . The mechanism of the M dust /M and M H2 /M decline, whose timescale suggests active galactic nucleus (AGN) or low-ionization nuclear emission-line region (LINER) feedback, may also be preventing the large CO-traced molecular gas reservoirs from collapsing and forming denser star forming clouds.