“Pray the ʿishāʾ prayer any time between now and one-third of the night; if you wish, you may extend it until half the night, and do not be among the heedless.”
This chain is exceedingly sound.
As for what al-Ṭaḥāwī transmitted through Sufyān al-Thawrī, from Ḥabīb b. Abī Thābit, from Nāfiʿ b. Jubayr, that ʿUmar wrote to Abū Mūsā: “Pray the ʿishāʾ prayer whenever during the night you wish, and do not neglect it,” this contradicts the preceding report. The defect lies in the break between Ḥabīb and Nāfiʿ, for although Ḥabīb is trustworthy, he was known for frequent mursal transmissions and for tadlīs, as noted in al-Taqrīb. Here he merely says “from” without explicitly stating “he narrated to me,” so this report is not admissible—especially since it opposes what the reliable narrators have transmitted.
This view is also attributed to Mālik, as recorded in Bidāyat al-Mujtahid (75), and it is the position of Abū Saʿīd al-Iṣṭakhrī, who said: “When a third or half of the night has passed, the prayer is lost and must be made up.” Al-Shīrāzī mentioned this in al-Muhadhdhab. It is likewise the apparent wording of Imām al-Shāfiʿī in the chapter “Facing the Qiblah”: “If a third of the night has elapsed, I regard the prayer as missed.” Al-Nawawī comments in Sharḥ al-Muhadhdhab (3/40): “Some of our scholars agreed with al-Iṣṭakhrī on the basis of this explicit text, while the majority interpreted it otherwise.”
I add: One of the proofs Shāfiʿī cited for setting the limit at one-third of the night is the ḥadīth of ʿĀʾishah, who said: “The Messenger of Allah ﷺ delayed the ʿatamah (ʿishāʾ) prayer one night, so ʿUmar called out to him, ‘The women have fallen asleep…’”