I think the way you've displayed it will work properly and people will understand it. However, I would suggest to remove the save button, because there won't be anything to save in the first image. Make this button the "change information" button, and once a person clicks this button, you change it to "save changes".
Not every user might notice the fact that the button has changed, since the button is going to change at the same moment the fields change, and they will be focusing on the change in fields, since this is what they are going to use next.
Grouping elements which do roughly the same will also improve user experience and usability, if you want to know more about this you should lookup the Gestalt principles.