Yes, if you move to Denmark again, lets say two weeks before graduation, then you can become member of an A-kasse.
However, thats not automatically the same as you have the right to receive Unemployment benefits ("Dagpenge") after graduation.
For being eligible for getting Dagpenge after the special rule for graduates, you must:
- have had a permanent address in Denmark no later than one day before you commenced on your education/master at SDU, and
- be in Denmark again no later than 14 days (including weekends) after you end your education/graduation
You do not need to stay in Denmark during your education.
You dont tell us if you were living in Denmark when you commenced at SDU, so therefore we can not tell if you are eligible for Unemployment benefits.
But if you did, and you are an EU/EEA citizen, then there should be no problem about becoming a member of an A-kasse (when you are back in Denmark), and
also getting Dagpenge after graduation.
There is no requirement of prior memberhip periods for graduates. You only must remember to sign up at latest 2 weeks after graduation in
order to gain the graduate rights.
Let me know, if you need more information.