Hi,
you need to prove that you actually were living here (like a signed tenancy agreement, bills showing that you were paying rent). The best - most easy for you - and the normal procedure when you move would be to register your new address with the public authorities ("Folkeregistret"). If you have done that, off course the A-kasse would have no problem to verify from what date you were living in Denmark.
Best regards,
Anders, www.a-kasser.dk