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The astrophysical origins of $r$-process elements remain elusive. Neutronstar mergers (NSMs) and special classes of core-collapse supernovae (rCCSNe)are leading candidates. Due to these channels' distinct characteristictimescales (rCCSNe: prompt, NSMs: delayed), measuring $r$-process enrichment ingalaxies of similar mass, but differing star-formation durations might proveinformative. Two recently discovered disrupted dwarfs in the Milky Way'sstellar halo, Kraken and \textit{Gaia}-Sausage Enceladus (GSE), affordprecisely this opportunity: both have $M_{\star}\approx10^{8}M_{\rm{\odot}}$,but differing star-formation durations of ${\approx}2$ Gyrs and ${\approx}3.6$Gyrs. Here we present $R\approx50,000$ Magellan/MIKE spectroscopy for 31 starsfrom these systems, detecting the $r$-process element Eu in all stars. Starsfrom both systems have similar [Mg/H]$\approx-1$, but Kraken has a median[Eu/Mg]$\approx-0.1$ while GSE has an elevated [Eu/Mg]$\approx0.2$. With simplemodels we argue NSM enrichment must be delayed by $500-1000$ Myrs to producethis difference. rCCSNe must also contribute, especially at early epochs,otherwise stars formed during the delay period would be Eu-free. In thispicture, rCCSNe account for $\approx50\%$ of the Eu in Kraken, $\approx25\%$ inGSE, and $\approx15\%$ in dwarfs with extended star-formation durations likeSagittarius. The inferred delay time for NSM enrichment is $10-100\times$longer than merger delay times from stellar population synthesis -- this is notnecessarily surprising because the enrichment delay includes time taken for NSMejecta to be incorporated into subsequent generations of stars. For example,this may be due to natal kicks that result in $r$-enriched material depositedfar from star-forming gas, which then takes $\approx10^{8}-10^{9}$ years tocool in these galaxies.

Evidence from Disrupted Halo Dwarfs that $r$-process Enrichment via Neutron Star Mergers is Delayed by $\gtrsim500$ Myrs