None of the first provided advice in Google resolved the mentioned issue on my computer, but I found the solution.
The incorrect behavior obviously caused by migration from 32bit to 64bit version.
We need just to replace the incorrect paths to the Firefox main executable image in the Windows registry:
1) Open Registry editor (regedit.exe);
2) Place focus on the root of registry database (My Computer);
3) Initiate text search (Ctrl+F). Specify "Parameter Value" flag only, and reset the rest flags.
4) Enter the next text to the search pattern field: "C:\ Program Files (x86)\Mozilla Firefox\firefox.exe" and press Search button to find first occurrence, all the next occurrences could be found by pressing consequentially F3 key.
5) Replace all incorrect occurrences with next string "C:\ Program Files\Mozilla Firefox\firefox.exe". This version doesn't contain "(x86)" string.
That is all.