1 PhD student, 2 institutions...1 of them completely closed to talking I want to get some advice about this difficult situation concerning one of my PhD students. 

Some time ago I wrote already about my status: I am assistant professor in Germany and very recently I got an offer for another permanent position abroad. I accepted it and in some weeks I will move there. 

The problem I have is the following: my PhD student is paid from my personal grant that will be lost the time I will move (let me say that until very recently I didn't know that I could not move this grant, in part because I was not well advised. So now I do not have margin of negotiation with my new institution). However, I have had an agreement with the Department of the old institution and they will pay him from the remaining money of this personal project that I won in a competitive way (namely, this is not money from the department, strictly speaking).

The problem goes when I propose to the department a cotutoring: this means that I would be the advisor in my new location, and the head of my group (who completely agrees) to be the second advisor here. There are plenty of agreement between universities (at least in Europe) on this form, and in my new affiliation they are very happy about this idea and they have already provided the general agreement they use.

The problem comes from my previous institution: they just say NO from administration, and they do not give any other choice for this. So: what should I do? This seems to me very unhelpful, even more considering that the money will finish at the end of the year and a coadvising would help on the search of extra money.

Also, this would mean that officially they are proposing me to "forget" of being his official PhD advisor (after 1,5 years of work, which is half of the PhD this is unfair from their part towards me...).

How should I deal with this situation?

Let me mention that the main idea for this coadvising was that in this way we could ask for funding in a coadvising setting. This is necessary as in some months the money will be gone, and we need to get extra money for him to finish (6 months- 1 year)

Thank you
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.