If we assume that the 2 "parts" should be regarded as individual educations, then it is correct that you can not start receiving unemployment benefits before 18 months after starting last education. This is also the case, even if you have graduated 27.06.
This has been clarified in recently updated legislation in this area.
But I understand that you off course would like to have the two parts being regarded as one full education, and by this way dont need to "wait for the 18 months to go", before you can get Unemployment benefits.
To be able to answer this in a proper way, I should know more about the two programs you have completed.
But I have tried to find information on the internet about the AP degree: An AP Degree is comparable to the first two years of a 3-year Bachelor Degree. Because of this, AP Degree Programmes also qualify graduates for further studies at universities or business schools in Denmark or abroad.
So, what I found out is that the AP Degree qualify for further studies.
I'm not sure that this is what is meant in the above excerpts from our website:
"den første del af uddannelsen er en nødvendig forudsætning for den næste del af uddannelsen".
And it is not possible for me to say if the subject from the one program are linked to the other. I can see that is is within the IT-field, but I am not sure that it is what we would normally perceive as a professional context.
I if was you, I off course would try to draw FTFa's attention on § 53, stk. 3, nr. 2 and § 54, and argue that your two programs whould be considered as 1 education.
I am not sure I can help you more on this topic, because this is out of the scope of our competencies and the objective with our website.
What you could have done to avoid the "problem" you are now facing, would be to have yourself registered as a graduate in your A-kasse after you had finished the AP Degree. Within two years after you are enrolled as a graduate, you can apply for Unemployment benefits. So in you case this could have been a solution if you have been guided when you finished you AP Degree.
Your are welcome to comment and we would try to help further if needed.