I don't see any charring other than the connector. Inspect the other side of the board once it's removed. If okay and you are handy, you can try fixing it.
You'd want to unsolder the burnt connector, get
somebody else's 12-pin in-line connector (it will be hard to find an exact replacement), wire that to the board, and splice the other side to the cable.
Before plunking down $25 or so for the connector, you could do a splice to see if it's worthwhile. Or you could skip the connector and keep the splice forever. Your call.
If you want to go ahead with a board replacement, my manual has part number as R0467600. I can't recommend a specific source, but will say clone electronics are usually not worth the trouble. Go for an OEM part. The
one listed on Amazon seems real, but counterfeits exist.
Disclaimer... Although I'm an EE and amateur electronics tech, I don't know this system well. I own one, but - knock on wood - it has been fine so far.