old galactic ages $\la 10^9$ yr, when the black hole has grown enough for its X-ray luminosity to be detectable at substantial redshift ($z>1$). This constitute a successful pilot study of the coevolution between black hole and galaxy growth at high redshifts, in a low X-ray luminosity regime associated to the early stages of galaxy evolution.

The two strongly-lensed galaxies analyzed in this work feature (intrinsic) SFRs of several $10^2\,M_\odot$ yr$^{-1}$ corresponding to far-IR luminosities $L_{\rm FIR}\ga 10^{46}$ erg s$^{-1}$; the stellar masses $M_\star$ are $\sim10^{11}\, M_\odot$, implying (for nearly constant SFR, see Papovich et al. 2011, Smit et al. 2012, Citro et al. 2016) rather young ages $\tau_{\rm age}\approx M_\star/$SFR of a few $10^8$ yr. As such, in the SFR vs. $M_\star$ diagram at $z\sim 2$, these galaxies are slightly offset with respect to the main sequence locus (Rodighiero et al. 2011, 2014; Speagle et al. 2014; see Fig.\[fig:main\_seq\]). This is due to the fact that the main sequence locus has been classically defined for mass-selected samples, while the galaxies considered here are far-IR selected; mass selection tends to pick up starforming galaxies at the end of their main star formation period, when their age is $\tau_{\rm age}\la 1$ 