He takes a down payment on the price of the item, then he buys it and hands it over to the purchaser

What is meant by taking a down payment from the purchaser is that the transaction is done and is made binding on both parties, so the deal has gone beyond the stage of discussing and bargaining, and has reached the stage of actually making a sale transaction. But it is not permissible for the Muslim to sell that which is not in his possession. 

Hakeem ibn Hizaam (may Allah be pleased with him) used to sell in this manner in the marketplace, and he asked the Prophet (blessings and peace of Allah be upon him) about it, and he told him not to do that. 

Abu Dawood (3503), at-Tirmidhi (1232) and an-Nasaa’i (4613) narrated that Hakeem ibn Hizaam (may Allah be pleased with him) said: I asked the Prophet (blessings and peace of Allah be upon him): O Messenger of Allah, a man may come to me and ask to buy something that I do not possess, and I sell it to him, then I buy it for him from the marketplace. He said: “Do not sell that which you do not possess.”

Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi

But if there is no agreement between the seller and the buyer, and it is simply a promise to sell or buy, without it being binding upon either of them, then there is nothing wrong with your buying the product after that and selling it to him, because the transaction is not complete until after you have taken possession of the item. 

Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him) was asked about a car dealer who said that he sold cars on the basis of monthly instalments, meaning that he would make an agreement with the person who wanted to buy a car by instalments, because he needed to do that, and he would agree on the sale with him before buying the car for him, primarily in order to guarantee his profits. What is the ruling on that? 

He replied:

If he sells the car or whatever to the one who wants to buy it after the seller takes possession of it, and it is put in his name and he moves it to his location, then there is nothing wrong with it. But selling it before that is not permissible, because the Prophet (blessings and peace of Allah be upon him) said to Hakeem ibn Hizaam: “Do not sell that which you do not possess.” And he (blessings and peace of Allah be upon him) said: “It is not permissible to do two transactions in one (such as lending in return for a sale at a particular price), or to sell that which you do not possess.” These are both saheeh hadiths, so it is obligatory to act in accordance with them and to avoid that which is contrary to that. And Allah is the source of strength. End quote. 

Majmoo‘ Fataawa ash-Shaykh Ibn Baaz (19/21)

He was also asked: What is the ruling on what is known as “promise to buy”? Does it come under the heading of riba (usury)? 

He replied: 

The promise to buy is not a purchase; rather it is a promise to do so. If a person wants to buy something, and he asks someone to buy it and then sell it to him, there is nothing wrong with that, if he buys the item and takes possession of it, then sells it after that to the one who wants to buy it. It says in the hadith that was narrated from Hakeem ibn Hizaam (may Allah be pleased with him): – and he quoted the hadith mentioned above – – this indicates that if he sells it to his brother after taking possession of it, and it comes into his possession, there is nothing wrong with that.

End quote from Majmoo‘ Fataawa ash-Shaykh Ibn Baaz (19/68) 

Shaykh Muhammad ibn ‘Uthaymeen (may Allah have mercy on him) was asked about some shops nowadays where a person can go to buy an item from the seller, and the seller tells him to wait a moment, then he goes and brings the item from another shop. What is the ruling on that? 

He replied: 

If they make a binding contract to that effect, then that is not permissible, because the Prophet (blessings and peace of Allah be upon him) said: “Do not sell that which you do not possess.” But if they make a mutual promise, and he tells him to come back after ‘Asr, for example, and he asked for it in the morning, with the intention that he is going to buy this item, and he sells it to him after ‘Asr, there is nothing wrong with that, because there was no binding contract. What matters is that there should be no binding contract between them before the item is actually available and present. End quote. 

Liqaa’aat al-Baab al-Maftooh (115/24) 

With regard to the questioner saying: “and the payment of the remaining amount is made by monthly instalments with interest”, if what he means is that in the event of the monthly payment being delayed, interest will be added to it, this is haraam, and is riba (usury).

But if what he means is that the price of the item paid by instalments is higher than the price paid in cash, and that this additional amount is included in the monthly instalments, then this is permissible and there is nothing wrong with it, so long as both parties have agreed on the price and the contract is based on that. 

But it is extremely makrooh (disliked) to work that out as riba is worked out, such as if the seller were to say: I will increase the price by 20% every year. 

Rather the seller should work out the price by instalments, then inform the purchaser of that, and they should reach an agreement on that; it should not be likened to riba. 

Please see also the answers to questions no. 1847, 40000, 117808, 10958 and 135427

And Allah knows best..