The Hijr is part of the House, because the Messenger of Allah ﷺ performed tawaf around the House from behind it, and Allah said, "and let them circumambulate the Ancient House" [Hajj 22:29].
الحجر من البيت؛ لأن رسول الله ﷺ طاف بالبيت من ورائه، وقال الله: {وليطوفوا بالبيت العتيق} [الحج: ٢٩].
Ibn Khuzayma (2740) and Bayhaqi (5/90) both narrated it from the hadith of Sufyan, from Hisham bin Hujayr, from Tawus, from Ibn Abbas, and he mentioned it. Its chain is hasan because of Hisham bin Hujayr al-Makki, about whom there is disagreement, though his hadith is hasan.Ayesha said, "I do not care whether I pray in the Hijr or in the House." Abu Yaala narrated it, Maqsad Ali (587), with a sahih chain.