Oceankaj to Malmo

I have determined that if we want to go to Malmö we have to take a bus and train to the Copenhagen Airport, change trains, and go through a passport check. When we buy our 4 zone tickets at the Oceankaj convenience store or from the bus driver, will our tickets be good to Malmö or will we have to buy tickets at the Airport when we change trains?

First of all its only 3 zones to the airport.

But the cheapest thing will be to buy a 2 zone ticket and get the bus to Østerport or Nørreport and from there buy a ticket to Malmö.

The train to Sweden departs from these stations every 20th minute you just have to get off at the airport, do the ID check and reboard the train.

Since Østerport is under reconstruction its probably better to get the 25 bus to Nørreport instead because I´m not sure if there is a ticket shop at Østerport, I´m thing that there are only ticket machines.

This is what I have found.

https://www.tripadvisor.com/ShowTopic-g189541-i218-k7705926-Around_the_Sound_ticket-Copenhagen_Zealand.html

http://www.visitcopenhagen.com/copenhagen/transportation/tickets-prices

http://www.visitcopenhagen.com/copenhagen/around-sound-gdk412377

Danish Viking can hopefully give a more comprehensive and conclusive answer.

Oh DV replied while I wast typing.