In the context of this research work, we study the so-called problem of full snapshot reconstruction in hybrid antenna array structures that are utilized in mmWave communication systems. It enables the recovery of the snapshots that would have been obtained if a conventional (non-hybrid) Uniform Linear Antenna (ULA) array was employed. The problem is considered at the receiver side where the hybrid architecture exploits in a novel way the antenna elements of a uniform linear array. To this end, the recommended scheme is properly designed so as to be applicable to overlapping and non-overlapping architectures. Moreover, the full snapshot recoverability is addressed for two cases, namely, for time-varying and constant signal sources. Simulation results are also presented to illustrate the consistency between the theoretically predicted behaviors and the simulated results, and the performance of the proposed scheme in terms Angle-of-Arrival (AoA) estimation, when compared to the conventional MUSIC algorithm and a recently proposed hybrid version of MUSIC (H-MUSIC).