Strongly recommend you get a AC VOLTMETER and make some measurements like shown in this pictorial.
Make these measurements at the 120VAC RECEPTACLE where your SHORE POWER CABLE plugs into it.

Since you have been using it already with no smoke it most likely is OK but I would want to know for sure. There are so many BAD STORIES on here where the son-in-law or best friend does the work. Its best to use the licensed and BONDED electrician so their insurance will pay the bill to replace all things that burns up when wired like the HOME systems are wired....
Roy Ken