Anyone who is a citizen of a non-EU/EEA country, but who is a family member of an EU/EEA citizen with a right of residence in Sweden, does not need a work permit to work in Sweden. If the person will be in Sweden for more than three months, they must apply for a residence card.
The person does not need any documents from their employer when applying for a residence card.
As long as the EU/EEA citizen has the right of residence, a family member of an EU/EEA citizen may start working right away and does not have to wait for a decision regarding their application for a residence card.