The Spectrograph System (SpS) of Subaru Prime Focus Spectrograph is fed by 2400 fibers and consists of four identical spectrograph modules with 4 arms and 600 fibers each. This paper outlines the overall integration process for the spectrograph module series as completed at the Subaru Telescope. Many partners from the Subaru PFS Collaboration and industry contributed to this large multi-object spectrograph system. The initial integration of the so-called "one-channel prototype" began in 2015. The first spectrograph module was delivered to Subaru in 2019, and the fourth module was delivered in late 2023, with delays due to both technical difficulties and scheduling challenges, including the impact of COVID-19 on the large PFS spectrograph system collaboration. The integration and validation of each spectrograph module were performed at the Laboratoire d’Astrophysique de Marseille (LAM) prior to delivery and full integration at the Subaru Telescope. First, we briefly review the opto-mechanical design and development strategy for the SpS. We present the integration and testing procedures developed for this mini-series of four spectrograph modules. Several specific AIT tools were innovative and key to the process, and are worth reporting, including the software tools required for functional tests, housekeeping, and environment monitoring during integration, analysis of dimensional metrology, test and verification of optical alignment, and overall performance assessment. Specific processes were also developed for analyzing and resolving anomalies and issues encountered. We detail the strategies developed to resolve technical issues: thermal and vacuum performance; dimensional and optical metrology processes to correct for focus/tilt anomalies observed at the focal plane; handling, alignment, and optical testing of large optics such as the 340x340x20mm Volume Phase Holographic Grating (VPHG). We briefly report on a grating orientation issue discovered before the delivery of the last module, which is reported elsewhere. We quickly report the integration logistics: managing the shipping process, custom, and deliveries of many parts and modules among partners since 2014, and the final delivery and installation at the Subaru Telescope at the summit of Mauna Kea in Hawai`i in 2019, 2022, and 2023. We then dedicate a full section to the optical and thermal performance for the largest 8m-class multi-object spectrograph: the spectral channels and camera alignment performance results and the detailed optical performance of the four spectrograph modules (extracted from internal extended performance reports).
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