Display screen with animated graphical user interface

FIG. 1 is a front view of a first image in a sequence for a display screen with animated graphical user interface in which messages presented within the animated graphical user interface are presented with a color gradient transitioning in color from an upper portion of the animated graphical user interface to a lower portion of the animated graphical user interface;

FIG. 2 is a front view of a second image thereof;

FIG. 3 is a front view of a third image thereof; and,

FIG. 4 is a front view of a fourth image thereof.

The appearance of the animated graphical user interface sequentially transitions between the images shown in FIGS. 1-4 . The process or period in which an image transitions to another forms no part of the claimed design. The broken lines corresponding to a mobile device and display screen forms no part of the claimed design. The remaining broken lines, including the closely spaced broken lines showing text, show portions of the graphical user interface that form no part of the claimed design.