We present a novel, virtual X-ray observatory designed to obtain synthetic observations from hydro-numerical simulations, named phox. In particular, we provide a description of the code constituting the photon simulator and of the new approach implemented. We apply phox to simulated galaxy clusters in order to demonstrate its capabilities. In fact, X-ray observations of clusters of galaxies continue to provide us with an increasingly detailed picture of their structure and of the underlying physical phenomena governing the gaseous component, which dominates their baryonic content. Therefore, it is fundamental to find the most direct and faithful way to compare such observational data with hydrodynamical simulations of cluster-like objects, which can currently include various complex physical processes. Here, we present and analyse synthetic Suzaku observations of two cluster-size haloes obtained by processing with phox the hydrodynamical simulation of the large-scale, filament-like region in which they reside. Taking advantage of the simulated data, we test the results inferred from the X-ray analysis of the mock observations against the underlying, known solution. Remarkably, we are able to recover the theoretical temperature distribution of the two haloes by means of the multi-temperature fitting of the synthetic spectra. Moreover, the shapes of the reconstructed distributions allow us to trace the different thermal structure that distinguishes the dynamical state of the two haloes.