Lets get an understanding. Synthetic shares do not exist on any list to be filled. They only exist when a short is closed the short holder needs to buy x number of shares. Whether they are real or imaginary, so to close the short position the holder must buy the shares back.
Synthetic shares implies that the MM that sold the short to the holder did not check if the shares are available to borrow. Implying they could be unreal/imaginary/synthetic/counterfeit/etc. One can not trade synthetic shares like they are real shares. They exist for closing short positions only.