This is a draft, details will follow ASAP - QII = After the summit. (Have to check semester date

Summer Semester in Berlin and Brandenburg: Lecture times vary a couple of days depending on the institution and state, but generally speaking 12th of April to 23rd of July, so June should be fine and far enough away from any exams to work.
List of Public Universities in Berlin/Brandenburg: Studieren in Berlin und Brandenburg (studieren-in-bb.de)