yes you always just stop being a member of an A-kasse. You can just call the A-kasse to cancel membership.
But remember that canceling A-kasse membership have serious consequences in the meaning that you will loose you seniority in the A-kasse, and will need to start from scratch again if you later want to become member again.
If you keep your membership, but you don't come back to Denmark after a jobsearch period in another EU/EEA-country then you cannot receive unemployment benefits in Denmark again before you have had at least 296 hours of work within a period of 12 weeks.
So you must be aware that is can have serious consequences if you do not return to Denmark after a 3 month job-search period in another EU-country.
But off course you can always quit membership and therefore also say no to receive any more unemployment benefits. And you do not need to provide any documentation to cancel a membership.
Anders Weber, www.a-kasser.dk