Emacs multi-term: backward||forward-word and kill-word

With the default configuration Emacs term moves only the emacs cursor but not the shell cursor when moving by words with default keybindings.  You can fix that by appending

'(("M-d" . term-send-forward-kill-word)

  ("M-DEL" . term-send-forward-kill-word)

  ("C-DEL" . term-send-forward-kill-word)
  ("M-<backspace>" . term-send-backward-kill-word)
  ("C-<backspace>" . term-send-backward-kill-word)
  ("M-<right>" . term-send-forward-word)
  ("C-<right>" . term-send-forward-word)
  ("M-<left>" . term-send-backward-word)
  ("C-<left>" . term-send-backward-word))

to custom valiable term-bind-key-alist.