when you change A-kasse it is the responsibility for the two A-kasser together to ensure:
1. that you don't pay membership fee for the same period in both A-kasser. In your case you will get money paid back from FRIE for a period of approx. 2 months.
2. Your aquired rights (membership periods, income/working hours etc) will be transfered to the new A-kasse
3. to inform Skat.dk (Tax), how much you have paid in membership fee. So you get the right amount to deduct in your tax.
If you are unemployed and receive dagpenge at the time you change A-kasse, you must accept that there will be a notice period, meaning that you may be transferred at the earliest with one month's notice until the end of a payout period. As unemployed on dagpenge it will therefore take some longer time before the change of A-kasse come into effect.
However you will still not pay memberhsip fee in both A-kasser at any time.
Anders Weber, www.a-kasser.dk