Problem is the invoice itself is real. You have to contest it actively to the debt collector and give at least some evidence as to why the debt is invalid. If you do not actively contest the collection, it will soon end up in court. This is a very routine case for a district judge where they will give a default judgement in favor of the plaintiff.
The problem is that the law in Finland is written so that even if the collection is baseless the supposed debtor needs to actively manage it or end up in legal jeopardy. Which is rather unfair if you are a victim of identity theft.