The Messenger of Allah ﷺ continued to recite the talbiyah until he threw the pebbles at Jamrat al-Aqaba.
حدثنا أحمد بن حنبل حدثنا وكيع حدثنا ابن جريج عن عطاء عن ابن عباس
أن رسول الله ﷺ لبى حتى رمى جمرة العقبة
Bukhari narrated it in Hajj, chapter on talbiyah and takbir on the morning of the sacrifice until stoning the jamrah, etc., no. 1685, and Muslim in Hajj, chapter on the recommendation for the pilgrim to continue the talbiyah once he begins it, no. 1280, from the hadith of Ibn Jurayj through this same chain, and it is in Musnad Ahmad, 213/1.