The code you are looking for is:
(define-key keymap-1 (kbd "new prefix")
(lookup-key keymap-2 (kbd "old prefix")))
You don't usually need to know the names of the keymaps as the expressions
(current-global-map) and (current-local-map) return the global and local maps in
force. Although the emacs manual says you can re-map any of the function keys, I have found that strange things can happen if you try to re-map f1, f2, f3, f4 or f10. For this reason I usually re-map f5 or f6. As an example from my .emacs file, the code:
(add-hook 'planner-mode-hook
#'(lambda ()
(local-set-key (kbd "M-RET") 'muse-insert-list-item)
(local-set-key (kbd "M-S-RET") 'pcomplete)
(define-key (current-local-map) (kbd "<f5>")
(lookup-key (current-local-map) (kbd "C-c C-j")))))
sets M-RET and M-S-RET in planner-mode and also makes the prefix
f5 into an alias for C-c C-j in that mode.
Be aware, however, that it doesn't
always work as lookup-key seem understand macros which, unfortunately, are
legal in keymaps. In such cases you can usually find a way round it. Ask again if
you have problems.