What is the authenticity of the hadith: "Does a believer commit adultery? He said: Yes. Does a believer lie? He said: No." And what is its text?

The Hadith (definition) was narrated by Imam Malik in Al-Muwatta' and mentioned by Imam Al-Ajlouni in "Kashf Al-Khafa' wa Muzil Al-Ilbas" with the wording: "It was asked: 'O Messenger of Allah, can a believer be a coward?' He said: 'Yes.' It was asked: 'Can he be stingy?' He said: 'Yes.' It was asked: 'Can he be a liar?' He said: 'No.'" It was also reported from Umar ibn Al-Khattab, may Allah be pleased with him: "You will not find a believer to be a liar," and from Sa'd ibn Abi Waqqas, raised [to the Prophet]: "A believer is naturally disposed to every characteristic except treachery and lying." Al-Bayhaqi mentioned the weakening of its raised status, and Al-Daraqutni preferred its halted status, but its ruling is that it is raised to the Prophet, according to the correct view, because a believer cannot be a liar, as stated in the Almighty's saying: "It is only those who do not believe in the verses of Allah who fabricate falsehood, and it is they who are the liars." [An-Nahl:105].