Also not a "i know this" but my "you could try", Menu apps file '.desktop' are stored in /usr/share/applications/ you can try to open firefox.desktop there with a text editor and modify the line Icon=firefox to your icon ;
My guess is any relative name like 'firefox' would link to the corresponding icon of the current theme so you should go with the absolute link to your image /home/your-name/Images/something.png or whatever ;
Same thing for System Software it is solus-sc.desktop