Hi,
according to the this page:
https://su.dk/su/om-su-til-videregaaende-uddannelser/godkendte-videregaaende-uddannelser
Erasmus Mundus degree (Global Forestry) is NOT an education program approved by SU.
Also I can see on another page (https://www.ug.dk/uddannelser/bachelorogkandidatuddannelser/kandidatuddannelser/naturvidenskabeligekandidatuddannelser/oevrigenaturvidenskab/global-forestry)
that the education has a participation fee, but that you can apply for SU.
According to these sources I will assess that you can NOT get graduate rights in the A-kasse.
However, I will strongly recommend you to also ask an A-kasse.
About the requirement of stay in Denmark. You only have to have stayed in Denmark before the education startet and again at latest 2 weeks after the education is finished. During the education you can stay outside Denmark.
The CPR is not relevant when we talk rules about Unemployment benefits (“dagpenge”) – so it dosen’t matter that you have been de-registered from the CPR-register.
The income must be reported to the income register within 12 months during the last 24 months.
The work does not need to have been carried out for 12 consecutive months, but wage hours must be reported in each of the 12 months.
Hope it helps.
Best regards,
Anders Weber, A-kasser.dk