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The matter - anti matter asymmetry observed in the universe today still lacks a quantitative explanation. One possibility that could contribute to the observed state could be a violation of the combined Charge-, Partiy- and Timesymmetries (CPT). To test if the CPT symmetry is broken the ASACUSA collaboration (Atomic Spectroscopy And Collisions Using Slow Antiprotons) at the CERN AD (Antiproton Decelerator) tries to produce a low temperature beam of antihydrogen - the most simple atomic system built only of anti particles. The ground state hyperfine splitting of hydrogen is one of the most precisely determined quantities in physics. Therefore it follows naturally to test CPT invariance by comparing the ground state hyperfine splitting of hydrogen and antihydrogen at zero B field. This contribution will focus on presenting the current state of the fully assembled spectroscopy beamline, including a field-ioniser chamber, a strip-line resonator microwave cavity, a super conducting sextupole magnet and a detector for counting antihydrogen annihilations. We will put a spotlight on the performance of the beamline and on the detection part of the spectrometer. Our spectroscopy apparatus was tested with a beam of cold hydrogen and these tests lead to a measurement of the GS-HFS of hydrogen whose precision is in good agreement with simulation. The newly developed detector is composed of a position sensitive Bismutgermanat (BGO) disc in the centre and a two layer hodoscope made of plastic scintillators that is read via silicon photo multipliers (SiPM) with self developed frontend electronics. In addition, our first preliminary results of the detector performance with the fully assembled beamline from the 2014 beamtime at CERN are discussed. ; Grant-in-Aid for Specially Promoted Research (No. 24000008) of the Japan Society for the Promotion of Science (JSPS), and Pioneering Project of RIKEN, European Research Council under European Union's Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement (291242), the ...