Okay so I've searched for similar posts but haven't found anything about my specific situation:

I have worked in California at the same company for the last 2.5 years. However, due to my partner's job change, we moved back to WA. My employer wanted to keep me on board and asked if I could work remotely. My first check, I noticed that WA taxes are taken out, but I'm confused because aren't I correct that they, as a company, would have to file a business license in WA state in order for me to be employed by them and pay WA taxes (they didn't). I will have zero travel to CA for any work purposes. Am I currently working illegally? My first week of pay after having moved they just cut me a check. If they don't register in WA, would I need to buy a business license and start being 1099'd ?

For info purposes, I do Marketing and Social Media for this company