Carroll geometries emerge as conformal boundaries of asymptotically flat spacetimes and have come to the forefront with the advent of flat holography. I will introduce these tools and show how they are used for unravelling the boundary manifestation of Ehlers' hidden Möbius symmetry present in four-dimensional Ricci-flat spacetimes that enjoy a time-like isometry. This is achieved in a designated gauge, where the three-dimensional Carrollian nature of the null conformal boundary is manifest and covariantly implemented. The action of the Möbius group is local on the space of Carrollian boundary data. Among these data, the Carrollian Cotton tensor plays a prominent role both in the Möbius electric/magnetic duality and for the determination of charges.