Praise be to Allah.
Yes, he has the right to do that. This was done by ‘Umar ibn al-Khattaab, and this is the view of Imam Ahmad (may Allaah have mercy on him).
Shaykh Ibn Baaz (may Allaah have mercy on him) said:
There is nothing wrong with keeping the down payment, according to the more correct of the two scholarly opinions, if the seller and buyer had agreed to that and the sale had not been completed.
Fataawa li’l-Tijjaar wa Rijaal al-A’maal, p. 49
It says in Fataawa al-Lajnah al-Daa’imah, 13/133:
Making down payments is permissible; that is when the buyer gives the seller or his agent a sum of money that is less than the price of the goods, after the agreement is made, to guarantee that he will get the goods and no one else will take them, and when the goods are delivered, this down payment is to be regarded as part of the price. If he does not then buy the goods, the seller may take the down payment and keep it, and the transaction is valid, whether he stipulated a time for payment of the rest of the price or not. The seller has the right to ask the purchaser to pay the rest of the price once the transaction has been completed and the goods have been handed over. The fact that making down payments is permissible is indicated by the fact that ‘Umar ibn al-Khattaab (may Allaah be pleased with him) did that. Imam Ahmad said concerning making down payments: There is nothing wrong with it. And it was narrated that Ibn ‘Umar (may Allaah be pleased with him) regarded it as permissible. Sa’eed ibn al-Musayyib and Ibn Sireen said: There is nothing wrong returning the product if he did not like it and giving something with it. With regard to the hadeeth that was narrated from the Prophet (peace and blessings of Allaah be upon him), saying that he forbade making down payments, this is a da’eef (weak) hadeeth which was classed as such by Imam Ahmad and others, and it cannot be taken as evidence.