If your departure ZZZZ is outside EGKK's CTR, but within R112, you must first establish 2-way R/T with Atlas; it will co-ordinate the handover to EGKK when appropriate.
When you lift from your ZZZZ inside the EGKK CTR, you should call EGKK by phone before lifting, or by radio from the hover (or tight orbit), giving it your authorisation number, etc. and it will co-ordinate and hand you over to Atlas (on a non ICF) when you exit its zone.