Had the same issue for days and figured it out today:
You need to submit the session cookie, which you will find in the "set-cookie" header of your GET request.
This needs to be passed to the POST request. Unfornately this can't be done using a custom connector.
I used a normal http request for this. You can set a Cookie Attribute there.
For the info from "set-cookie" you need to replace "," with ";" before passing it to your POST-Request.