Should I return the money to the buyer after I was scammed by a fake company, knowing that the company took the money from me and the buyer is demanding it from me?

The transaction mentioned is not Sharia-compliant because it involves selling something you do not own or possess. This is a form of gharar (uncertainty) and gambling, which can lead to disputes. The Prophet (peace be upon him) forbade selling what one does not possess. In addition, it is not permissible to sell a commodity before acquiring it and transferring it into the seller's possession or warehouse.

To rectify the transaction so that it complies with Sharia, one of two methods can be followed: 1. "Promise to sell" (Bay’ al-Muwāʿadah): You display the goods to the buyer who expresses a desire to purchase them, and you determine a price, with no obligation on either party to sell or buy until you legally acquire ownership of the commodity. Then, the contract is finalized. 2. Being a broker: You sell the goods for a fixed commission or a specific percentage of the price in return for your effort.

As for the money paid to you by the woman, it must be returned to her, and her right to it is binding upon you regardless of whether you are able to recover your money from the company.