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Use the Lasso Tool to select the other badge image. Be careful this time. Try not to include any of the background color in your selection.

Cut the selected badge and Paste it slightly to one side of the shadow.

Look for clues in the original image that will tell you what direction the light is coming from.

Use the Paint Brush Tool to fill in any open areas that might be missing a shadow.
And presto whammy! An officer's badge that would make any bad guy quake and shake.