Display screen or portion thereof with animated card communication interface

FIG. 1 is a first image in a sequence for a display screen or portion thereof with animated graphical user interface showing the new design;

FIG. 2 is a second image thereof; and,

FIG. 3 is a third image thereof.

The appearance of the animated images sequentially transitions between the images shown in FIGS. 1 through 3 .

The process or period in which one image transitions to another forms no part of the claimed design.

The long-dashed lines forming a portion of a rectangular shape in FIGS. 1 through 3 are included in the claimed design.

The short-dashed broken line showing of a display screen or portion thereof with animated card communication interface is included for the purpose of illustrating portions of the article and forms no part of the claimed design. The short-dashed showing a device is included for the purpose of illustrating environmental structure and forms no part of the claimed design.