The first thing would be the distance between A & C. That has to be 12' or less for it to be legal to remove B. Is one of those receptacles on a switch for some reason?
Because box B is about 3 feet up the wall. I don't want to cover it I want to remove it from the circuit. She had a stereo system in an ugly built-in I removed.
What are the two "Inbound"? There's no sense in that drawing -- if A & B are on separate circuit for redundancy in the room (reasonable if were there for lighting and no permanent fixtures in room), then the run between A & B doesn't make sense.
As other said, you can't get rid of the cover plate anyway unless you convert to one junction box and rewire to eliminate the splice in the B box location so you don't gain anything of significance by just pulling out the receptacle and replacing it with a blank cover in my view. What's it hurt, anyway?
Here is the issue. You can't have a splice in a concealed location. It must be accessible. That means you have to put a cover plate over it. A cover plate looks worse than a receptacle. So that makes what you want to do so difficult that from a practical standpoint, it's not worth it. To do it without leaving a cover plate you're going to have to run a new wire between the two remaining outlets, which typically requires opening the wall. At that point, aside from all the wall work, the electric part is trivial.
Another option would be to put a cover plate on it, then hide it with a picture or similar, but then you're back to being able to do that with the receptacle that's already there.
Right simple to run a wire, the wire to box C is accessible and I could easily pull it. I am just asking how to eliminate box B. Its seems inline with box A and C, so running another wire seems simple...except I can't explain the extra wire that enters the bottom of box B.
W/O being able to see what's inside A and B and knowing for sure who's actually power (altho one might presume the "HR" means "home run", we can't tell from only what we can see for sure.
I'd guess one can _probably_ find a way to pull new run from C to A bypassing B entirely and then removing the whole thing, but we can't see enough to tell.
The point is making that a run w/o a splice is the only allowed way -- splicing the existing wires and removing the face plate and hiding the box behind the wall board is NOT allowed.
If you can't figure it out to make the straight run, two acceptable alternatives I see would be
Replace single duplex A with double and move B to the one location side by side -- same number outlets but one less box; or
IF the other side of the wall is accessible and not otherwise undesirable, mount B facing the other direction in other area.
We can't see what's connected to what. You seem to treat these cables as all incoming, but that may not be the case. Where do they go? Like someone asked, is one from a switch? Or does one that you've called incoming actually power something else? Like the wire into A is the feed, with the wire from B going to another receptacle, light, etc? Or B being the feed and the A wire going to power something else?
At it's simplest, even without understanding what's connected to what, which could make it simpler, just remove the receptacle and keep the existing connectivity exactly the same using the boxes at A and C. I saw the pic showing the wall is open, so this is easy.
Yeah, that's good point -- other than depending on how many connections/pigtails have to have, may need a deep box to cram it all in one. But, it'll work.
_Almost_ certain can simply string a cable between A and C, but just not possible to know for certain while the boxes are still all covered up...
Code requires any wiring splice to be permanently accessible. That means you need to replace the entire run between the remaining boxes in order to completely remove the middle box.
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