The flight model of the laser system for the Mars Organic Molecule Analyzer (MOMA) instrument within the ExoMars 2020 mission for Martian planetary surface exploration has been developed, assembled, tested, and finally integrated to the NASA Goddard Space Flight Center (GSFC) mass spectrometer. The nanosecond laser system consists of a longitudinally pumped, passively Q-switched Nd:YAG based laser oscillator with a two-stage frequency doubling to 266 nm. The laser design was implemented in robust and lightweight models of the laser head (LH) with the pump unit in a separate electronics box. In parallel to the laser head integration and testing, materials and optics qualification and acceptance tests have been performed, e.g. to determine the optical damage threshold or the susceptibility to laser induced contamination processes. Before delivery to the NASA GSFC for integration to the mass spectrometer (MS) flight model (FM), the laser system has been qualified in an environmental test campaign including vibration, shock and thermal-vacuum testing. After delivery to GSFC and integration to the FM MS, the system has been successfully re-tested on the instrument level.