1 PhD student, 2 institutions...1 of them completely closed to talking
I find your question a bit negative. It appears that you are blaming your current university for not giving you more support as you leave for your new university. Further, and potentially more problematic, is that you appear to be treating the student like a pawn. Have you asked the student what they want? Comments like


  after 1,5 years of work, which is half of the PhD this is unfair from their part towards me...


it is also extremely unfair of you to leave a student hanging out to dry halfway through a PhD. This is a student's worst nightmare.
I think it is important to realize that first and foremost, you screwed up. You did not adequately negotiate, prior to signing a contract, appropriate support for your current student. It surprises me that you are switching from one permanent position to another, yet you did not manage to secure enough startup funds to support a PhD student for 1.5 years.

To an extent, your new department is not being supportive. While you screwed up and did not realize that some of your grant money could not come with you, they are not willing to cover a student for 1.5 years. This is potentially problematic. Do you really want to work for a department that will not cover for you when you make mistakes?

Your current department has done nothing wrong as far as I can tell. Potentially, they were not as clear as they could have been about the grant funding, but you do not tell us much about that. Your current department needs to look out for its faculty and students. Paying for a student to work at another university is generally not in the best interest of the department. This is especially true if there are adequate supervisors in the current department.

Moving forward, I would suggest you talk to the student. Find out what the student wants. They might want to move completely to the new department. Similarly, they might want to cut ties with you. Maybe they want you as a co-supervisor. Once you know what the student wants, you, and to an extent you and the student, can ask for it. As for you, expecting to get anything "back" from the student and the time spent supervising the student, is a little unrealistic in this situation.