What is the ruling on a partner waiving their share of a house, which was bought with mixed funds from an internet café, to their brother in order to observe Sharia regulations, and not demanding compensation, with the intention of changing the work to something that pleases Allah?

Earning money from internet cafes that are used for what Allah has forbidden is not permissible. If this service is rented out with knowledge of the unlawful purpose for the cafe's patrons, then the collected rent is not lawful. The earner must repent, seek forgiveness, and dispose of the unlawful money by spending it on good deeds and giving it to the poor and needy. As for what was bought with this money, he owns it and is not obligated to sell it; he only needs to dispose of the amount of the unlawful money. If he is poor and does not possess this amount, or is in need of it for his basic necessities, we hope that repentance and seeking forgiveness will suffice him.