Is the apartment mentioned in the question rightfully owned by the questioner according to Islamic law? Is the uncle's ruling, that the apartment be sold and the questioner be given his capital plus half of the profit generated from the price increase, valid according to Islamic law? What is the Islamic legal ruling on the uncle's action of purchasing the apartment with his own money without informing the questioner, despite the questioner having sent him money to buy it, and then the uncle claiming that the price increase is exclusively his right?

If the uncle informed his nephew that he had bought the apartment for him, acknowledged it to him, and showed it to him as his own, and the nephew paid the price, then the apartment is his right, and the uncle is only entitled to what he paid on his behalf. If the nephew has evidence, he should present it to the courts. If not, he may demand an oath from the uncle. If the uncle swears that it is his, then the apartment is his, and he must return the price to his nephew. If he refuses to take the oath, then the apartment belongs to his nephew. Reconciliation is not obligatory as long as it is not satisfactory, but reconciliation is better. It is not permissible for the uncle to wrong his nephew. They can agree to sell the apartment and divide the profit, knowing that the profit belongs to the owner of the apartment. Knowing the details requires hearing the claims of the litigants in court.