The Xport and SharkPort V2 software now saves the icon with the file (thus allowing it to restore saves without needing an existing save) but..
It doesn’t store the games icon, rather it replaces every icon in the save (saves contain up to three icons) with it’s own. Using PS2 Save Builder you can now inject the correct (or even a more interesting) icon back into the save. Icons are found either on the disc in case of GTA: VC (a rare occurrence though) or can be extracted from other saves. Please note that some .psu/.psd saves are a backup of an Xport save and may possably contain the incorrect icon. If so, search again for another version of the save.
A patch is available for the Xport software, applying it stops the software from injecting it’s own icon and leaves the original icon intact