Insurance intermediaries that are authorized in another EEA State may conduct financial activities in Sweden if it is within the scope of a relevant EU Single Market Directive. In order to do so, the institution must first contact its home-state regulator which will notify Finansinspektionen.
For further information regarding national rules that an insurance intermediary needs to comply with, see this link (https://www.fi.se/en/insurance/apply-for-authorisation/notification/).
There are also additional national rules known as ”general good provisions”. General good provisions are national rules of the Member States which introduce additional requirements addressing specificities of the respective markets and have to be observed by market participants providing cross-border services into that market. See further information on these provisions in Sweden in an edited EIOPA-report from 2019 here
For general guidance purposes, see also handbook developed through Bipar on cross border insurance distribution:
https://www.bipar.eu/en/page/bipar-handbook-on-cross-border-insurance-distribution