Yes you could connect to the connector or the receptacle, but I wouldn't go to the receptacle when an opening is available on the connector. Actually I never spliced through a receptacle in a commercial project (which I assume this is because of the data jack).

For me it would be pretty hard to fish Armor Clad cable into the box and properly ground in the self-grounding cable connectors without access to the outside of the box. I would look to find a 1/2" knock-out and use MC cable and pigtail the ground from the MC cable to the box and receptacle.

It looks like the receptacle has clamp connections (not stab-backs based on no release tabs on the receptacle), if they are clamps they are just fine to use. It also looks like stranded wire, do not wrap stranded around any screws, you would have to use stake-ons, the clamps backs are better.

Also since the wire is marked 12 AWG the breaker is probably a 20A breaker, 12 AWG is the minimum size tap allowed in most jurisdictions.

Yes you could connect to the connector or the receptacle, but I wouldn't go to the receptacle when an opening is available on the connector. Actually I never spliced through a receptacle in a commercial project (which I assume this is because of the data jack).

For me it would be pretty hard to fish Armor Clad cable into the box and properly ground in the self-grounding cable connectors without access to the outside of the box. I would look to find a 1/2" knock-out and use MC cable and pigtail the ground from the MC cable to the box and receptacle.

It looks like the receptacle has clamp connections (not stab-backs based on no release tabs on the receptacle), if they are clamps they are just fine to use. It also looks like stranded wire, do not wrap stranded around any screws, you would have to use stake-ons, the clamps backs are better.

Also check breaker size, if the wire is #12 like the pigtail wires it may be a 20A breaker, and #12 is the minimum size in most jurisdictions.