How can I move from Copenhagen to Berlin?

Via Hamburg. Check the DB planner for timetables.

Thus this is a quite a detour, it will take nearly all day as there is no nighttrain for now-maybe again in summer. As for now you also MUST reserve seats in all DSB=danish IC trains-for free if you can understand danish at their site, this is for covid-distance rules.

There will also be more direct buses-via a ferry that takes a few hours,

Or if you feel very adventurous: take train via bridge/tunnel to Malmö-change for Ystad and use 1 of 2 ferries (POlferries or Unity line-both give a little discount)-to Swino-ujscie in PL-then train to Szczecin (which is much easier to say as you think)-then train to Berlin. Ferries go by day and overnite.

You could also try to search for the Nighttrain of Snälltåget from the airport of Copenhagen or from Malmö to Berlin. Reservation compulsory.