This conversion looks like export of navigation / map data from Google Earth format (.kmz) and saving it in a raster map format from Garmin (.jnx). It should be possible with programs, such as MAPC2MAPC converter, that are designed for map conversions.
Convert Compressed Keyhole Markup Language (Google Earth) data to Garmin raster map.
We found one software available in the database for this conversion.
Microsoft Windows software - convert kmz to jnx on Windows
A digital map conversion software
Convert from kmz file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.