Having internet problems. I didn't see the lack of an OPSPEC, only the lack of the type requiring an SIC. He could log SIC if they don't have the 135.105 exemption or a working autopilot. Regardless of what the actual PIC put in his logbook, the sole manipulator is the ONLY pilot that can log PIC.

Interesting fact that probably doesn't apply: Some 200s and 300s required a second pilot.