  We present the commissioning of the Fast Annihilation Cryogenic Tracker
detector (FACT), installed around the antihydrogen production trap inside the 1
T superconducting magnet of the AE\=gIS experiment. FACT is designed to detect
pions originating from the annihilation of antiprotons. Its 794 scintillating
fibers operate at 4 K and are read out by silicon photomultipliers (MPPCs) at
near room temperature. FACT provides the antiproton/antihydrogen annihilation
position information with a few ns timing resolution. We present the hardware
and software developments which led to the successful operation of the detector
for antihydrogen detection and the results of an antiproton-loss based
efficiency assessment. The main background to the antihydrogen signal is that
of the positrons impinging onto the positronium conversion target and creating
a large amount of gamma rays which produce a sizeable signal in the MPPCs
shortly before the antihydrogen signal is expected. We detail the
characterization of this background signal and its impact on the antihydrogen
detection efficiency.
