Is the prayer valid for someone who leaves the prayer after the final sitting without giving salām?

According to Imam Abu Hanifa, the person performing the prayer must exit the prayer at the end by performing an action with their own will and intention. According to Imam Abu Yusuf and Muhammad, however, sitting for the duration of the tashahhud (enough time to recite the tahiyyat) completes the prayer in terms of its pillars. Even if the person does not give salām or does not intentionally perform an act that invalidates the prayer, their prayer is still valid, but a necessary (wājib) act has been omitted.

This difference of opinion has some legal consequences. Accordingly, if a person, after sitting for the duration of the tashahhud in the final sitting (qa'da al-akhira), intentionally performs an act incompatible with the prayer—such as responding to a greeting, saying “bless you” or “yarhamukallah” to someone who sneezes, or getting up and leaving—the prayer is valid according to all three imams mentioned. (Marghinani, al-Hidaya, 1/60-61; Zayla'i, Tabyin, 1/104; Bilmen, Ilmihal, 118) However, if the prayer is broken after sitting for the tashahhud due to a reason beyond the person's control, the prayer is valid according to Imam Abu Yusuf and Muhammad, but not valid according to Imam Abu Hanifa. Again, if the prayer time ends after sitting for the tashahhud in the final sitting, but before the person intentionally exits the prayer, the prayer is valid according to Imam Abu Yusuf and Imam Muhammad, but invalid (fāsid) according to Imam Abu Hanifa. (Kasani, Bada'i, 1/127; Ibn al-Humam, Fath al-Qadir, 1/386)

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu