Is it permissible for him to inherit property that was bought with a riba-based loan?

If a person takes out an interest based loan and buys
property with it, when he dies the property becomes part of the estate which
is inherited from him, but he has sinned by dealing in riba. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: 

What is haraam because of the way in which it is acquired is
haraam for the one who earns or acquires it, such as riba. But if the person
who dealt with riba dies, then his wealth is permissible for his heirs. What
is haraam in and of itself, such as alcohol, is haraam to the one who
acquires and to the one to whom he passes it on. Similarly, if a person
steals something or seizes it by force then dies, it is not permissible for
his heir (to take the stolen property); if he knows who it belongs to he
must return it, otherwise he should give it in charity on behalf of the
owner. 

From Liqaa’aat al-Baab al-Maftooh, 1/304 

The Standing Committee
issued a fatwa concerning a person who built a house with a riba-based loan,
stating that he has to repent and seek forgiveness, and that he does not
have to destroy the house; rather use may be made of it by him or someone
else living in it. 

Fataawa al-Lajnah al-Daa’imah,
13/411. 

And Allaah knows best.