TPS was officially extended for nationals of El Salvador. The extension is automatic through January 4, 2021. This means that work authorization is automatically extended as well. TPS recipients can demonstrate the Federal Register notice to employers as a confirmation of their work authorization extension.
Current TPS recipients who live within the jurisdiction of the Ninth Circuit Court of Appeals (This includes California, Arizona and Nevada among others) and are married to a United States citizen or are the parents of a United States citizen over the age of 21 can apply for the lawful permanent residency without having to leave the country. It is important to act on this as soon as possible.