Hello!

I need to move files to another location and to update all symbolic links to this location. Can any file manager like Dolphin or Konqueror automatically do this for me

So you want the file manager to find and update all symbolic links on the system that were pointing to the old location and update them to the new location? or do you mean update any symbolic links in the files being moved?

In either case I don't know of any file manager that will do that. You could probably do that with scripts. Of particular interest is the "find" command's -lname parameter which allows you to search for symbolic links whose link matches the given pattern. The find command then has a -exec parameter which you can use to evaluate another command for each matching file found.
"find /path/to/directory/with/symlinks/to/update -lname /original/path/* -exec updateLink.sh {} /original/path /new/path ;"
Where updateLink.sh is another script which updates a given link to point from the original path to the new path.