Anybody have experience moving to Spain with employment by a European (but not Spanish) company?

I am a Californian moving to Madrid, currently employed by a Swedish company, with whom I will have continued employment after the move. I have been a remote worker since moving from NY last year, and will be a remote worker in Madrid. The "Notification of work and residence permit approval (COMUNICACIÓN DE CONCESIÓN DE AUTORIZACIÓN DE TRABAJO Y RESIDENCIA)" is generally discussed in the context of working for a Spanish company. Any advice?