Quote from “as-Samtu Thamin fi manaqib Ummahat al-Muminin” (p 27), by Muhib ad-Deen at-Tabari:
The shiahs hold (opinion) that a prophet’s property is also inherited and these houses (of the wives) were inherited by his wives. This contention is false and even if that was so they would have got only one eight share. Sayidah Fatimah would have got half share while the remaining would have gone to the asbah (relatives on the father’s side). However, we come across no evidence of anyone having received a share of having waived his or her share, or permission sought from any of the asbah to bury Sayydina Umar (in the house of Aisha), or to enclose the houses in the mosque.
Further it is also baseless to say that the houses didn’t belong to prophet’s (sallalahu alaihi wa ala alihi wa sallam) wives but they only had the right to stay there. We do know that Sayyidah Sawdah had left her house for Sayydidah Aisha and Sayyidah Safiyah’s house was sold by her heirs. Sayyidah Aisha had also sold her house with the stipulation that she would reside there as long as she was alive.
Most of the scholars contend that the houses belonged to the wives of the prophet (sallalahu alaihi wa ala alihi wa sallam) and they had not inherited them.