Is it permissible for the father to sell his property to one of his sons and not the other?

Firstly: 

If the father intended, by selling this property to one of his sons and not the others for a very cheap price, to show preference towards this son over his brothers and to single him out to acquire some of his property by means of a superficial commercial transaction, this is a haraam trick to commit sin and transgression. It is not permissible for the Muslim who is about to meet Allah — as he has reached the age of 80 — to do this, thus causing resentment and grudges among his sons and going against the command of the Prophet (blessings and peace of Allah be upon him) who said: “… Fear Allaah and treat your children fairly.” Narrated by al-Bukhaari (2398) and Muslim (3055). 

But if your father did not intend to do such a trick; rather he actually wanted to sell his property to any purchaser as your brother claims, because he was in urgent need of the money, then he should sell it for the market price, and there is nothing wrong with his reducing the price a little for his son, as people customarily do such things when involved n similar transactions.  

If more than one of a man’s children wanted to buy his property and all of them wanted to buy it for a similar price, then he should cast lots among them, and the one whose name is drawn will have the right to buy the house, so as to avoid any hint of favouritism towards one of his sons with regard to giving and so that all his sons will be free from resentment, grudges, shunning and envy towards one another. 

Secondly: 

If the father did do wrong and favoured one of his sons, and the others did not approve of that, then it is their right to object to that sale and to ask him to cancel it. They could offer to help him financially, if he needs it, in the form of a loan, if he really was in need of money; or they could ask him to treat them fairly with regard to giving, either by giving all of them property like he gave to that son, or by sharing out among them from his wealth and giving an amount equal to the difference between the price for which his son bought the house and the price for which similar properties are usually bought.  

Thirdly: 

We would remind all of you brothers that the ties of kinship that exist among you are greater than this insignificant worldly matter and such matters should not lead you to hate one another. With regard to what has happened among you of differences, strive to remove the causes of that in the best manner, and give precedence over everything else to the ties of kinship that existed between you. 

Shaykh Saalih al-Fawzaan (may Allah preserve him) was asked the following question:

I am a man whom Allah has decreed should suffer some disease in his right leg and the doctors have decided to amputate it, which means that I will not be able to work, and I am the head of a large family. I have three brothers, but my father has sold his farmland to my three brothers. Because I am unable to buy any part of it, I did not get anything. It is what my father did valid or do I have the right to ask for my share without buying or selling? 

He replied: 

If he sold this farmland to your brothers in a valid transaction in which there was no trickery or compulsion — rather he sold it to them as he would sell it to anyone else for the full price, and he did not let them off any part of the price; rather he received the price in full from them — then there is nothing wrong with that and you do not have the right to object, because there is no favouritism involved in that and he was not singling them out for any money and excluding you. 

But if that was not the case, and it was a sale that involved trickery and he was lenient towards them concerning that and showed favouritism towards them, then that is not permissible, because it is unfair and the father must treat his children equally with regard to giving gifts, and it is not permissible for him to single some of them out to the exclusion of others, because the Prophet (blessings and peace of Allah be upon him) said: “… Fear Allaah and treat your children fairly.” The father is obliged to treat the children fairly with regard to giving gifts to them, and it is not permissible for him to favour some of them over others. End quote. 

Majmoo’ Fataawa al-Shaykh Saalih al-Fawzaan, 2/594, 595 

And Allah knows best.

See also the answer to question number 114659 and 119655.