Assalaamu ‘Alaykum wa Rahmatullaahi wa Barakaatuh.
Some people say that the Hadeeths of the Prophet, sallallaahu ‘alayhi wa sallam, were recorded after a long time, maybe centuries after the Prophet, sallallaahu ‘alayhi wa sallam, had died. Therefore, inauthentic texts were added to the Hadeeths. Will you please explain this issue?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.

It is not true that the Prophetic traditions and Hadeeths were recorded  centuries after the Prophet, sallallaahu ‘alayhi wa sallam, had died. The Companions would write down and memorize Hadeeths during the lifetime of the Prophet, sallallaahu ‘alayhi wa sallam. Hadeeths were consequently transmitted by the Tabi’ees (the followers of the Companions), and the process of general documentation of Hadeeths began during the era of ‘Umar ibn ‘Abd Al-‘Azeez who himself was a Tabi‘ee.

It is true that irrelevant texts were added to Hadeeths. However, the scholars distinguished fabricated texts and set accurate standards and rules that remain unequalled in all fields of knowledge and are exclusive to the Islamic sciences. They stipulated the continuity of Hadeeth transmission through a chain of upright and accurate narrators in the sense that each narrator had heard the Hadeeth from the narrator who preceded him in the chain, and that the text be free from all hidden defects that negatively affect its authenticity, and that it does not contradict another narration by a more trustworthy narrator. If even one of these conditions was not satisfied, the Hadeeth would be rejected.

Further details can be found in books on Mustalah Al-Hadeeth (Hadeeth Terminology and Criticism). Also, scholars have authored numerous books on Hadeeths classifying them as weak, fabricated, authentic or acceptable.