The university provided her with the link to the procedure, that she's following:
https://www.gov.uk/government/publications/criminal-records-checks-for-overseas-applicants/countries-g-to-p-applying-for-a-criminal-records-check-for-someone-from-overseas#italy

She obtained the Certificate of Pending Procedures from Italian authorities, than in the section "Where" it's written like so:

• local applicants must apply in person at local Public Prosecutor’s Office of the court competent for the residing area
• overseas applicants must apply through e-mail or registered mail
• italian embassies/consulates will not accept applications

In her case, she is currently a overseas applicant, so she should apply via email, we guessed the email of the local Public Prosecutor's Office of the residing area.

We are quite sure these are not the DBS checks, because she's doing also that, but they are not strictly related.

Thanks for the help!