FARR (Flyktinggruppernas Riksråd) is an independent umbrella organization for individuals and groups working to strengthen the right to asylum in Sweden.
Their website has general information on migration law and asylum procedures in Swedish as well as a dedicated section for people fleeing from Ukraine in English, Ukrainian, and Russian.
They publish a very comprehensive guide for asylum seekers in Sweden called „Goda Råd“.
You can get it as a PDF in various languages here.
They also operate a counseling hotline for refugees: +46 8-710 02 45
