FelixUrbasik The group is here: https://www.facebook.com/groups/Karlekarinteturism. Unfortunately it’s a closed group, so one cannot see the posts there without being a member.
As for evidence that the intent is enough, someone in the group shared an email he got from the Ministry of Justice saying so (although the email also clearly says that it does not work if you only are in a relationship with someone, i.e. a "non-serious" one). Also, https://polisen.se/en/the-swedish-police/the-coronavirus-and-the-swedish-police/faq/ says under "Family connections"
What is considered a close family connection?
Foreigners whose intention is to enter into marriage or a common-law/cohabitation partnership with, if they can document previous physical contact (e.g. with photographs) and that the relationship is serious.
but unfortunately there are other questions in this FAQ which give somewhat contradictory answers, so it’s not entirely clear…
As for how it is proven, I have no idea :) For instance having applied for a residence permit (even if it hasn’t been granted yet) should be enough proof, but hopefully it should be possible to convince them of that even without having applied for a residence permit yet. Most of the stories in the group connect through Denmark/Germany/UK though, so I guess that the authorization to enter Europe is then given by those countries’ interpretation of Swedish law…