If your friend paid directly to the Estonian bank maybe they can look up for the sortcode (there are tools online) to find the bank. If not, and from experience, Estonian institutions are super cooperative and reply really fast. I would turn to Politsei.eeEestipank.ee in case nothing else works.

But definitely it would be better if the police could provide the name of the bank in Estonia, it will most likely be LHV or Swedbank, which are also very quick to try solving situations like this. I hope your friend can get their money back!