My suggestion is to use hook_form_alterhook_form_FORM_ID_alter
to add a custom submit handler. In that submit handler, you will get the current menu item values. Use those values to create a new menu item for the other menu.
Functions to use:
- hook_form_FORM_ID_alter. Here form id will be 'menu_edit_item'
- Use form['#submit'][] = "custom submit handler" in form alter.
- Use menu_link_save in custom submit handler based on the values you get form the form_state.