  Studies based on imaging the annihilation of the electron (e$^{-}$) and its
antiparticle positron (e$^{+}$) open up several interesting applications in
nuclear medicine and fundamental research. The annihilation process involves
both the direct conversion of e$^{+}$e$^{-}$ into photons and the formation of
their atomically bound state, the positronium atom (Ps), which can be used as a
probe for fundamental studies. With the ability to produce large quantities of
Ps, manipulate them in long-lived Ps states, and image their annihilations
after a free fall or after passing through atomic interferometers, this purely
leptonic antimatter system can be used to perform inertial sensing studies in
view of a direct test of Einstein equivalence principle. It is envisioned that
modular multistrip detectors can be exploited as potential detection units for
this kind of studies. In this work, we report the results of the first
feasibility study performed on a e$^{+}$ beamline using two detection modules
to evaluate their reconstruction performance and spatial resolution for imaging
e$^{+}$e$^{-}$ annihilations and thus their applicability for gravitational
studies of Ps.
