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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 mm data to confirm their presence and relative role in contributing to the galaxy SEDs and energy budget. We present the data, model and analysis in the X-ray and mm bands for two strongly lensed galaxies, SDP.9 and SDP.11, selected in the Herschel-ATLAS catalogues as having an excess emission in the mid-IR regime at z>1.5, suggesting nuclear activity in the early stages of galaxy formation. We observed both of them in X-ray with Chandra and analyzed the high-resolution mm data available in the ALMA Science Archive for SDP9, and, by combining the information available, we reconstructed the source morphology. Both the targets were detected in the X-ray, strongly indicating the presence of highly obscured nuclear activity. High resolution ALMA observations for SDP9 in continuum and CO(6-5) spectral line allowed us to estimate the lensed galaxy redshift to a better accuracy than pre-ALMA estimates and to model the emission of the optical, mm, 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. Hence, 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., Accepted for publication on A&A