A friend of mine sent me this link to an official Italian government website which mentions (Google Translate translation):
From December 15, 2021, the validity of the COVID-19 green certification for vaccination, for doses following the first or dose after recovery, passes from 12 to 9 months from the date of administration. Check when you have taken the last dose, if more than 9 months have passed, you are among those who would find themselves without COVID-19 Green Certification as a result of this variation. Book your booster dose by December 14, 2021, and you will receive the new Certification within 48 hours of administering the vaccine, which will be valid for 9 months.
Does it mean that access to Italy will be limited to those with <9 months of vaccine validity?