It might be possible to open JPEG2000 images in GIMP or similar graphics editor and save them as icons in ICON format.
Convert JPEG 2000 (ISO 15444-1) picture to Icon image file.
We have found 3 software records in our database eligible for .jp2 to .icon file format conversion.
Microsoft Windows software - convert jp2 to icon on Windows
A free graphics and photo editor and authoring tool
Convert from jp2 file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned jp2 to icon. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Apple macOS / Mac OS X software - convert jp2 to icon on OS X
Mac version of the popular graphics editor
Linux/Unix software - convert jp2 to icon on Linux
GNU Image Manipulation Program