Following Taranis' failure during its launch in 2020, an R&T development program has been started in 2021 by the team that developed the XGRE gamma-ray spectrometer onboard Taranis, at the Astroparticle and Cosmology (APC) laboratory (Paris, France). This program, funded by the French Space Agency (CNES), aims to develop a new gamma-ray spectrometer for space applications, and especially for the detection of Terrestrial Gamma ray Flashes (TGFs) from space. Aimed to be a multi-mission detector, Fast Gamma ray Spectrometer (FGS) can be adapted to different scientific objectives, using the same technology, namely a GaGG scintillator coupled with a Silicon Photo-Multiplier (SiPM) and an ASIC to read the signal. It is now based on 16 crystal pixels of 2 cm × 2 cm × 1 cm, but can be optimized to fit the mission purposes, FGS being used for different scientific objectives such as Gamma Ray Bursts (GRBs) and solar flares. In that sense, the GaGG scintillator type, the size of the scintillator pixels, and the number of pixels can be thus different for each mission. During the development, we consider TGFs, which are the most constraining events that we aim at, to define the detector characteristics: rapidity, energy range, timetag of photons. GaGG scintillators are newly developed non-hygroscopic scintillators, with a high light-yield and a fast decay time. We studied three different GaGG versions in the present work: a mean, a high spectral resolution, and a fast GaGG crystals. In order to validate the choice of the scintillator used, we show in the present work a comparison of their performances, and measurements within the ARRONAX proton accelerator to simulate the degradation due to the South Atlantic Anomaly (SAA) passages. FGS performances concerning TGF detection are also presented.