We study the evolutionary path of the Fornax Cluster galaxy NGC 1436, which is known to be currently transitioning from a spiral into a lenticular morphology. This galaxy hosts an inner star-forming disc and an outer quiescent disc, and we analyse data from the MeerKAT Fornax Survey, ALMA, and the Fornax 3D survey to study the interstellar medium and the stellar populations of both disc components. Thanks to the combination of high resolution and sensitivity of the MeerKAT data, we find that the H I is entirely confined within the inner star-forming disc, and that its kinematics is coincident with that of the CO. The cold gas disc is now well settled, which suggests that the galaxy has not been affected by any environmental interactions in the last ~1 Gyr. The star-formation history derived from the Fornax 3D data shows that both the inner and outer discs experienced a burst of star formation ~5 Gyr ago, followed by rapid quenching in the outer disc and by slow quenching in the inner disc, which continues forming stars to this day. We claim that NGC 1436 has begun to effectively interact with the cluster environment 5 Gyr ago, when a combination of gravitational and hydrodynamical interactions caused the temporary enhancement of the star-formation rate. Furthermore, due to the weaker gravitational binding H I was stripped from the outer disc, causing its rapid quenching. At the same time, accretion of gas onto the inner disc stopped, causing slow quenching in this region.