Modern co-evolutionary scenarios between supermassive black holes and their host galaxies predict that nuclear activity and star formation are strictly related and time-coordinate processes. Dusty star-forming galaxies (DSFGs) play a key role in the study of this interplay, as they constitute the bulk population at the peak of cosmic star formation. Far-infrared (FIR)/sub-mm surveys proved to be an extraordinarily efficient tool to select samples of lensed DSFGs, which are ideal targets for follow-up observations aimed at studying, down to sub-kpc scales, the detailed properties of objects otherwise not exceptionally bright or peculiar. This, coupled with radio band observations, provides information on processes that govern the FIR- radio correlation (FIRRC), linked with the star-formation activity and the possible AGN presence. In this seminar I will present the FIRRC for a sample of high-redshift (1