Hi,
you tell you have been employed PhD with a salary.
So according to unemployment benefits, you should use the normal rules for salaried.
So you must have had at least 52 weeks (1.924 hours) of work within the last three years and been a member of an unemployment insurance fund for at least one year.
Only paid work on "nomal conditions" (I assumes PhD salary is) is counted and only work conducted during membership periods is counted. We assume you have had the paid PhD during the last 12 months you have being paying to A-kasse.
If you have continious been paing to the A-kasse for at least 12 months an continue to do that, then you can apply for unemployment benefits as soon as you have the permission to work full time in Denmark.
Best regards,
Anders, www.a-kasser.dk