If it's a vector graphic in Ilustrator format, and not just a graphic embedded in Illustator, then this will work:
Choose the graphic and then in the color pallet: add selected colors.
Create a third color as a placeholder for the white.
Draw a box and make the fill and stroke the white color that was added to your pallet.
Select>same>stroke color and change to your placeholder color
Select>same>Fill color and change to your placeholder color
then follow the same procedure to change the red to white, and the placeholder color to red.
Hi there - Do you know if this original file is a vector image? The file you linked to is a rasterized .png file. If the original is a .png raster image, you can easily alter the colors in Photoshop.