Chromospheric LAyer Spectro-Polarimeter (CLASP2) is our next sounding rocket experiment after the success of Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP1). CLASP2 is scheduled to launch in 2019, and aims to achieve high precision measurements (< 0.1 %) of the linear and circular polarizations in the Mg ii h and k lines near the 280 nm, whose line cores originate in the upper solar chromosphere. The CLASP2 spectro-polarimeter follows very successful design concept of the CLASP1 instrument with the minimal modification. A new grating was fabricated with the same radius of curvature as the CLASP1 grating, but with a different ruling density. This allows us to essentially reuse the CLASP1 mechanical structures and layout of the optics. However, because the observing wavelength of CLASP2 is twice longer than that of CLASP1, a magnifier optical system was newly added in front of the cameras to double the focal length of CLASP2 and to maintain the same wavelength resolution as CLASP1 (0.01 nm). Meanwhile, a careful optical alignment of the spectro-polarimeter is required to reach the 0.01 nm wavelength resolution. Therefore, we established an efficient alignment procedure for the CLASP2 spectro-polarimeter based on an experience of CLASP1. Here, we explain in detail the methods for achieving the optical alignment of the CLASP2 spectro-polarimeter and discuss our results by comparing with the performance requirements.