The final stage of transition to turbulence in a supersonic flat-plate boundary layer at Mach 3 is investigated using Direct Numerical Simulations (DNS). A set of six simulations was performed to study the development of a pair of oblique waves from their initiation at low amplitudes to final breakdown to turbulence. In a previous paper (part I of this study), the linear and early nonlinear regimes of this so-called "oblique breakdown scenario" were discussed. The focus of the present paper (part II) is on the early turbulent regime, i.e. the region of the flow downstream of the maximum of skin friction. In this region, the flow is shown to have lost periodicity in time and to exhibit the typical mean flow and spectral properties of a turbulent boundary layer as known from the literature and theory. The DNS data clearly demonstrate that oblique breakdown can lead to a fully developed turbulent boundary layer and therefore may be a relevant mechanism for practical applications. authors.