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Based on observations with the $Chandra$ X-ray Observatory, we present the latest spectral evolution of the X-ray remnant of SN 1987A (SNR 1987A). We present a high-resolution spectroscopic analysis using our new deep ($\sim$312 ks) $Chandra$ HETG observation taken in March 2018, as well as archival $Chandra$ gratings spectroscopic data taken in 2004, 2007, and 2011 with similarly deep exposures ($\sim$170 - 350 ks). We perform detailed spectral model fits to quantify changing plasma conditions over the last 14 years. Recent changes in electron temperatures and volume emission measures suggest that the shocks moving through the inner ring have started interacting with less dense circumstellar material, probably beyond the inner ring. We find significant changes in the X-ray line flux ratios (among H- and He-like Si and Mg ions) in 2018, consistent with changes in the thermal conditions of the X-ray emitting plasma that we infer based on the broadband spectral analysis. Post-shock electron temperatures suggested by line flux ratios are in the range $\sim$0.8 - 2.5 keV as of 2018. We do not yet observe any evidence of substantial abundance enhancement, suggesting that the X-ray emission component from the reverse-shocked metal-rich ejecta is not yet significant in the observed X-ray spectrum.