Pretend that a country within the European Union (EU) has refused to extradite somebody, after an extradition request from another country, following a court ruling in the extraditee's favour.
If the, now free, defendant wishes to travel to other EU countries, can they avoid extradition based on the ruling that was in their favour against extradition? Assume the extradition was for the same purposes as the original request for extradition.
My understanding is that EU countries must respect decisions in other EU member courts, so I am guessing this would also apply to extradition.
For the purposes of this question feel free to exclude places such as Norway and Switzerland, as they have their own distinct agreements with the EU.
EDIT: The defendant has a British passport and a Republic of Ireland passport making them dual nationality, however they entered into each EU country using their Irish passport.