How to get back to an active minibuffer prompt in emacs without the mouse

This will do what you want. Bind to the key of your choice:

(defun switch-to-minibuffer-window ()
  "switch to minibuffer window (if active)"
  (interactive)
  (when (active-minibuffer-window)
    (select-frame-set-input-focus (window-frame (active-minibuffer-window)))
    (select-window (active-minibuffer-window))))
(global-set-key (kbd "<f7>") 'switch-to-minibuffer-window)

C-x o 

Repeat as necessary.

C-x o runs the command other-window, which is an interactive built-in function in `C source code'.

If you do not want to cycle through windows, you can add a function in your init file and bind it to a key. Something like this might work:

(defun select-minibuffer ()
 "Make the active minibuffer the selected window."
 (interactive)
 (when (active-minibuffer-window)
   (select-window (active-minibuffer-window))))

Another option is using switch-window

I find it to be a really useful package: it allows you to quickly move to any Emacs window, visually (and I do use a lot of open windows in Emacs).

But I just find out it also allows you to move to the minibuffer, if it is active:

Hope it helps.

;; faster switching between windows in the same frame
(windmove-default-keybindings)

Adding two above lines of code to .emacs.el will enable simple and efficient moving, not just to minibuffer, but also navigating all other windows on Emacs frame using Shift-Arrow.