i live in EU. somebody from another EU country is writing me that they intend to take me to court for a very minor possible copyright infringement. my question is - if meanwhile i move to live in a completely different EU country, can he have success in court over there since the actual copyright infringement took place in a different country?
As user Philipp notes in a comment, international lawsuits can succeed. This is surely even easier within the EU than it would be otherwise. I do not precisely know how the proper venue would be chosen in the EU case you describe, but there is a Wikipedia article discussing the relevant regulation, the Brussels I Regulation:
The Brussels I Regulation contains a jurisdictional regime: the rules which courts of European Union Member States use to determine if they have jurisdiction in cases with links to more than one country in the European Union. The basic principle is that the court in the member state of the party that gets sued has jurisdiction, ...
There are, however, several exceptions to the basic principle.
Even if the action is pursued in the original country, any judgment arising from that action would be enforceable in the new country:
In 2012, the EU institutions adopted a recast Brussels I Regulation which replaced the 2001 regulation with effect from 10 January 2015. The recast regulation...abolishes formalities for recognition of judgments and simplifies the procedure for a court chosen by the parties to commence proceedings (even if proceedings have started in another member state already).
Therefore, the general answer to the implied question, whether one can avoid legal action for copyright infringement by moving to a different country, is no.