He hasn't committed one general offense of betting on football - every single individual bet is a separate offence.
The Italian FA can deal with any offences [bets] in Italy and apply a punishment. The FA can look into any extra potential offences in England.
And they should do to be honest. It's a general principle of law that you can't just pick and choose who they apply to. That just allows corruption.
Bit like if someone got punished for speeding offences in Italy, they move to the UK and get caught speeding here, they can't go 'well you can't punish me for speeding now, I've already been punished for when I was speeding back in Italy.'
If there are more offences though it could be that punishments already imposed are taken into account when deciding what new punishment is appropriate.