Aims. According to coevolutionary scenarios, nuclear activity and star formation play relevant roles in the early stages of galaxy formation. We aim at identifying them in high redshift galaxies by exploiting high-resolution and sensitivity X-ray and millimetre-wavelength data to confirm the presence or absence of star formation and nuclear activity and their relative role in shaping their SEDs and contributing to their energy budget. Methods. In the current paper we present the data, model and analysis in the X-ray and mm bands for two strongly lensed galaxies, SDP.9 (HATLAS J090740.0-004200) and SDP.11 (HATLAS J091043.1-000322) that we selected in the Herschel-ATLAS catalogues as having an excess emission in the mid-IR regime at redshift > ∼ 1.5, suggesting the presence of a nuclear activity in the early stages of galaxy formation. We observed both of them with Chandra ACIS-S in the X-ray regime and analyzed the high resolution mm data available in the ALMA Science Archive for SDP9, and, by combining the information available in mm, optical and X-ray bands we reconstructed the source morphology.Results. Both the targets were detected in the X-ray, strongly indicating the presence of highly obscured nuclear activity. ALMA observations for SDP9 for continuum and CO(6-5) spectral line with high resolution (0.02arcsec corresponding to ∼ 65 pc at galaxy distance) allowed us to estimate the lensed galaxy redshift to a better accuracy than pre-ALMA estimates (1.5753±0.0003) and to model the emission of the optical, millimetric, and X-ray band emission for this galaxy. We demonstrated that the X-ray emission is generated in the nuclear environment and it strongly support the presence of nuclear activity in this object. On the basis of the X-ray data, we attempted an estimate of the BH properties in these galaxies. Conclusions. By taking advantage of the lensing magnification we identified weak nuclear activity associated with high-z galaxies with large star formation rates, useful to extend the investigation of the relationship between star formation and nuclear activity to two intrinsically less luminous, high-z star forming galaxies than was possible so far. Given our results only for two objects, they solely cannot constrain the evolutionary models, but provide us with interesting hints and set an observational path towards addressing the role of star formation and nuclear activity in forming galaxies.