I am traveling to Italy more than 9 months since my booster. Will I be allowed into the country?
The 9 Months, more accurately 270 days, applies only to the original course of shots (two for most, one for the J&J). If you have a booster, there is no limit...at this time.
If for some reason a second booster is widely recommended, then they may change that, but likely not in the next 3 months or so.