Is taking the sum of 4,500 Saudi Riyals from the auctioneer forbidden (haram) or sinful, given that he paid the amount after it was proven that the car license the questioner bought was forged, and the car was impounded and returned to its owners, and that the auctioneer is not to blame for the forgery of the license, except that the bill of sale was drawn up in his auction house?

If the auctioneer donates the car's price to you, on the condition that he will later claim it from the seller, or if it is customary for the auctioneer to guarantee that the car reaches you and the price reaches the seller, this is called "warranty of liability or recourse" (ḍamān al-ʿuhdah aw al-darak). This is permissible according to the majority of scholars due to necessity. If this warranty is the prevailing practice in the auction, then there is no harm for you in taking the money. If the warranty of recourse is not practiced, then his donation is an act of benevolence from him, and you are permitted to accept it.