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Despite the ever-growing number of exoplanets discovered and the extensive analyses carried out to find their potential satellites, only two exomoon candidates, Kepler-1625b-i and Kepler-1708 b-i, have been discovered to date. A considerable amount of effort has been invested in the development of algorithms for modelling, searching, and detecting exomoons in exoplanetary light curves. In this work, we incorporate moon handling capabilities into the state of the art and publicly available code, the Transit and Light Curve Modeller (tlcm). The code is designed for the analysis of transiting exoplanet systems with the inclusion of a wavelet-based noise handling algorithm. Here, we present an updated version of tlcm that is capable of modelling a coplanar planet–moon system on an elliptical orbit around its host, accounting for mutual eclipses between the two bodies (and neglecting perturbative effects) – a so-called photodynamic model. The key benefit of this framework is the ability for a joint analysis of multiple planet–moon transits. We demonstrate the necessity of this software on a case study of Kepler-1625b. Similarly to prior works, we conclude that there is no firm evidence of an exomoon in that system, by showing that temporally correlated noise can mimic apparent lunar transits. [ABSTRACT FROM AUTHOR]