Hi Odysseus,
I’ve not had the pleasure of using either of these two instruments, let alone connecting them together to get useful information from the AIS.
However, looking at the web site
http://raymarinec80.com/raymarine_c80_manual/ I was able to look at both the installation guide as well as the user manual for the C80 plotter, while a further internet search revealed that the McMurdo M15 (
https://www.manualslib.com/manual/934350/Mcmurdo-Smartfind-M15.html) used the NMEA 0183 protocol as its output, and presumably has a cable coming from the instrument that you can connect to the plotter.
So far as I could determine from the plotter manuals, all you need to make the connection to the plotter is an NMEA 0183 plug which presumably you can get from your local Raymarine stockist, and note that the connections you would need to use are shown in one of the photos below and are marked on the right side of the plug as the NMEA 0183 +ve and -ve inputs.
The wiring diagrams do not show any other components being used between the AIS instrument and the plotter. When connecting AIS to my own plotter I had to use a device to convert NMEA 0183 to NMEA 2000, and that was a headache and a half !! Your plotter does not appear to use NMEA 2000.
Hopefully the attached screen shots of the different pages should help, you will then need to set the output from the AIS unit to the baud rate of 38400 as per the instruction from Raymarine and which is apparently the standard output from the McMurdo unit. Good luck.