Hi,
I assume that you canceled your membership in the danish A-kasse when you began job in the other EU country. And that you have been insured against unemployment when working in the other EU country.
If this is true, you can transfer your insurance period from the other EU country to the danish A-kasse when moving back to Denmark again.
Because you have been member in a danish A-kasse within the last 5 year period, you dont need to work in Denmark to be able to transfer your insurance periods.
You need a PD U1 document from the responsible authority in the other EU country. This PD U1 document have information about your insurance period. You must give this to the danish A-kasse. And the danish A-kasse will take in to account your insurance period in the other EU country when deciding if you meet the danish requirements for Unemployment benefits.
You can read more about PD U1 here:
https://www.a-kasser.dk/transfering-periods-of-work-and-insurance-from-another-eea-country/
You can see a PD U1 document here:
https://www.a-kasser.dk/formularer/eu/pd-u1-english.pdf
It is possible that the two countries involved can exchange the information electronically through EESSI, by so called Structured Electronic Documents (SED). Maybe ask the authority in the other EU country if they can do that.
I case of using EESSI you dont need a PD U1.
For being eligible for Unemployment benefits (“dagpenge”) from a danish A-kasse you must also meet the income-requirement. Please read more about all requirements here:
https://www.a-kasser.dk/requirements/
It is therefore also important that you are able to prove your income/salary for the period you have worked in the other EU country. This can be done with payment notes.
Please be aware that if you decide to quit your job your self (self-inflicted unemployment) you must accept a 3 weeks quarantine period, where you will not receive dagpenge.
Hope it helps you.
Best regards,
Anders Weber, A-kasser.dk