Strong gravitational lensing magnifies the light from a background source, allowing us to study these sources in detail. Here, we study the spectra of a $z = 1.95$ lensed Type Ia supernova (SN Ia) SN Encore for its brightest image A, taken 39 d apart. We infer the spectral age with template matching using the supernova identification (SNID ) software and find the spectra to be at $29.0 \pm 5.0$ and $37.4 \pm 2.8$ rest-frame days post-maximum, respectively, consistent with separation in the observer frame after accounting for time dilation. Since SNe Ia measure dark energy properties by providing relative distances between low- and high-z SNe, it is important to test for the evolution of spectroscopic properties. Comparing the spectra to composite low-z SN Ia spectra, we find strong evidence of the similarity between the local sample and SN Encore. The line velocities of common SN Ia spectral lines, Si II 6355 $\mathring{\rm A}$ and Ca II near-infrared triplet, are consistent with the distribution for the low-z sample as well as other lensed SNe Ia, e.g. iPTF16geu ($z = 0.409$) and SN H0pe ($z = 1.78$). The consistency between the low-z sample and lensed SNe at high-z suggests no obvious cosmic evolution demonstrating their use as high-z distance indicators, though this needs to be confirmed/refuted via a larger sample. We also find that the spectra of SN Encore match the predictions for explosion models very well. With future large samples of lensed SNe Ia, e.g. with the Vera C. Rubin Observatory, spectra at such late phases will be important to distinguish between different explosion scenarios.