For the ESA/Roscosmos ExoMars 2020 mission a pulsed UV laser source as part of the Mars Organic Molecule Analyzer (MOMA) instrument was developed, assembled and thoroughly tested concerning thermal, vibrational and shock loads. The characterization was performed before and after integration to a mass spectrometer, which serves as the detector for ionized fragments desorbed from the Martian soil samples due to UV irradiation. The opto-mechanical design of the flight model and the verification of its suitability for the mission requirements are presented here. A longitudinally pumped, passively Q-switched oscillator emits bursts of up to 50 pulses with an output energy of 1.1 mJ at 1064~nm and an intra-burst repetition rate of 100 Hz. Via a two-stage frequency quadrupling with a KTP and a BBO crystal this radiation is converted to 1.5 ns long pulses at 266 nm with an output energy of 130 µJ which can be decreased by temperature tuning of the nonlinear crystals to less than 10\% of the nominal energy. The laser head also comprises beam shaping and steering optics to adjust the spot size and position on the sample and the capability to measure the UV energy and the pulse release time. The complex opto-mechanical design is realized within an envelope of less than 220x57x45 mm³ and has a total mass of less than 220 g. To minimize negative effects of the harsh Martian environment on the coatings the laser head is enclosed in a hermetically sealed housing filled with dry synthetic air.