  We derive dust masses ($M_{\rm dust}$) from the spectral energy distributions
of 58 post-starburst galaxies (PSBs). There is an anticorrelation between
specific dust mass ($M_{\rm dust}$/$M_{\star}$) and the time elapsed since the
starburst ended, indicating that dust was either destroyed, expelled, or
rendered undetectable over the $\sim$1 Gyr after the burst. The $M_{\rm
dust}$/$M_{\star}$ depletion timescale, 205$^{+58}_{-37}$ Myr, is consistent
with that of the CO-traced $M_{\rm H_2}/M_{\star}$, suggesting that dust and
gas are altered via the same process. Extrapolating these trends leads to the
$M_{\rm dust}/M_{\star}$ and $M_{\rm H_2}/M_{\star}$ values of early-type
galaxies (ETGs) within 1-2 Gyr, a timescale consistent with the evolution of
other PSB properties into ETGs. Comparing $M_{\rm dust}$ and $M_{\rm H_2}$ for
PSBs yields a calibration, log $M_{\rm H_2}$ = 0.45 log $M_{\rm dust}$ + 6.02,
that allows us to place 33 PSBs on the Kennicutt-Schmidt (KS) plane, $\Sigma
\rm SFR-\Sigma M_{\rm H_2}$. Over the first $\sim$200-300 Myr, the PSBs evolve
down and off of the KS relation, as their star formation rate (SFR) decreases
more rapidly than $M_{\rm H_2}$. Afterwards, $M_{\rm H_2}$ continues to decline
whereas the SFR levels off. These trends suggest that the star-formation
efficiency bottoms out at 10$^{-11}\ \rm yr^{-1}$ 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
$M_{\rm dust}/M_{\star}$ and$M_{\rm H_2}/M_{\star}$ 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.
