Get user register form fields in edit profile form page
You can edit all forms in drupal using hook_form_FORM_ID_alter

So The only thing you need is the FORM_ID , to get that you can open any desired form , then using firebug or some tool like that you can recognize the ID of form.

in your special case the form ID of user edit form is : "user_profile_form" , so you can create a custom module and implement YOURMODULE_form_user_profile_form_alter()

inside print elements as you desire.