Converting Switched Plug to New Ceiling Lights - Wiring Help Need
I want to add 4 recessed ceiling lights to my collectibles room and run them off the existing light switch which currently controls one plug on one of the wall outlets. I am a newbie to this type of wiring so I am hoping that some of the experts can help me make sure to get this right. I have attached a picture showing how the existing outlet is wired as well as what I hope is the correct way to re-wire this for the ceiling lights.
The light switch currently has black/white/ground running to the switch. The wall outlet has black/white/ground coming into the bottom of the box and black/white/ground running out the upper left of the box which I think goes to the switch and another black/white/ground running out the upper right of the box which I assume is going to the next wall outlet. The interesting thing is that the one white wire that is in the wire nut bundle with all of the black wires does not have a piece of black tape or any marking on it to show it is hot.
Does the picture I attached of the proposed wiring look correct and safe?? I will of course have to install a new wall outlet as the brass connector between the two plugs is currently broken off to have a single switched plug.
Thanks for the help!!