The NHS "Covid Passport" only shows your first two vaccination details. The Prime Minister has suggested that if and when the need to prove vaccination status is brought into England, "fully vaccinated" may mean having had three jabs. Some countries are already using this interpretation in their entry requirements. So the government will be "looking into" the idea of having the booster jab added to your downloadable record. At some time. In the future. Perhaps. With a bit of luck and a following wind.