Ukrainian refugees can travel with their Ukrainian passport/ID card to Berlin, Dresden, Nuremberg and Munich. There is no need for a ticket.
If you wish to continue your journey, you can get a free “helpukraine” ticket valid in 2nd class to your desired destination at a DB Reisezentrum (DB Travel Centre) or at a DB agency. Please show your Ukrainian ID (passport/ ID card) to the ticket inspector on the train upon request.
further Info:
bahn.de/info/helpukraine