Holders of a valid research resident permit must request a permit of stay as "mobilità-ricercatore" by 8 days from their arrival in Italy to the local Police Headquarter (Questura).
Detailed information about research residence permit documents, application, etc can be found at Research residence permit webpage.
Please contact your Italian hosting oganisation at least 3 months in advance and refer to it in order to sign an hosting agreement and get the nulla osta (entry clereance) on due time.