He seized his sister’s house unlawfully then she died, and he is her only heir. Is the house permissible for him?

Firstly:

The one who usurps property is subject to a stern warning

The one who takes his sister’s house without her consent is a usurper and transgressor, who is subject to that stern warning, as al-Bukhari (3198) and Muslim (1610) narrated from Sa`id ibn Zayd ibn `Amr ibn Nufayl that the Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever seizes a handspan of land unlawfully, Allah will encircle his neck with it down through seven earths on the Day of Resurrection.”

Ahmad narrated that Ya`la ibn Murrah said: I heard the Prophet (blessings and peace of Allah be upon him) say: “Any man who seizes a handspan of land unlawfully, Allah, may He be glorified and exalted, will command him to dig it until he reaches the bottom of seven earths, then he will encircle him with it until the Day of Resurrection, until He passes judgement among the people.” Al-Albani classed it as sahih in as-Silsilah as-Sahihah, no. 240.

If his sister died without having forgiven him, but he has repented to Allah, then there is the hope that Allah will pardon him and that his sister will forgive him on the Day of Resurrection; otherwise, she will take some of his good deeds, as the Prophet (blessings and peace of Allah be upon him) said: “Whoever has wronged his brother, let him ask him for forgiveness, because there [in the hereafter] there will be no dinar or dirham. [So let him do that] before some of his good deeds are taken from him and given to his brother, and if he has no good deeds to his credit, some of his brother’s bad deeds will be taken and added to his burden.” Narrated by al-Bukhari, 6534.

Secondly:

Usurper inheriting what he seized unlawfully

If his sister died and he is her only heir, ownership of the house is transferred to him, and the ruling of having seized it lawfully no longer applies.

In al-Mawsu`ah al-Fiqhiyyah, 31/255, it says: The Maalikis said: The one who seized property unlawfully gains ownership of it if he buys it from its owner or inherits it from him. End quote.

And Allah knows best.