I really do not understand what you mean. Could you perhaps do a step by step illustration to reproduce the problem
you originally wrote
Is there any solution to fix Front-end modules herf is not being assigned to the menu/category
I just do not understand the connection between a 'module' and it being assigned to a menu or category
All your front end items seem to be in a module table as images with a link to the Download
The whole structure is nicely arranged in a grid Each column is a table and each row has a single cell with an image and a link to a Download.None of these are related to a menu item as they do not need to be. jD only comes into it when the Download is displayed.
At that point the browser shows "All Downloads|<Site Name>"
From that I assume you have a jD menu item All Downloads