It is narrated from Muhammad bin Ishaq (may Allah have mercy on him) that he said: "Musa bin Mitha bin Yusuf bin Ya'qub was born, and, according to what people claim, he claimed prophethood among the Children of Israel before Musa bin Imran. Those who are certain of this claim that he is the one (Musa) who sought out a scholar (Khidr, peace be upon him) in order to learn from him, until he found the scholar who made a hole in the boat, killed the boy and built the wall, and Musa bin Mitha was with him. Then he returned from him, until he attained what he attained." Imam al-Hakim (may Allah have mercy on him) says: Muhammad bin Ishaq mentions it this way, (whereas, in refutation of it) evidence is taken from the established and sahih hadith that Amr bin Dinar narrated from Sa'id bin Jubayr, who said: I said to Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both): Nawf al-Bikali claims that Musa, the companion of Khidr (peace be upon him), is not Musa bin Imran of the Children of Israel, but rather some other Musa. Sayyiduna Ibn Abbas (may Allah be pleased with them both) said: "The enemy of Allah (Nawf) has lied. Sayyiduna Ubayy bin Ka'b (may Allah be pleased with him) narrated to us that he heard the Messenger of Allah (peace and blessings be upon him) say: 'Musa bin Imran stood up to deliver a sermon among the Children of Israel'" (and then) he narrated the complete long hadith. This hadith is recorded in the two Sahihs (Bukhari and Muslim). What prompted me to mention it (here) is that I had left it out in the middle. As for Kalimullah Musa bin Imran:

It is narrated from Abayah al-Asadi that he said: I heard Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) say: Indeed Allah Almighty said in His Book to Musa bin Imran (peace be upon him): "(Allah said: O Musa!) Indeed I have chosen you above the people with My messages and My speech, so take what I have given you and be among the grateful." And He said: "And We wrote for him on the Tablets an admonition and a detailed explanation of everything." [Surah al-A'raf: 144 - 145] So Musa (peace be upon him) thought that all things had been established (fixed and made clear) for him, just as you people think that your scholars have made everything clear for you, and in the way they establish it. So when Musa (peace be upon him) reached the seashore, he met that scholar (Khidr, peace be upon him) and spoke with him, and Musa (peace be upon him) acknowledged the excellence of his knowledge and did not envy him; rather, Musa (peace be upon him) said to him, expressing his eagerness: "May I follow you on condition that you teach me some of the right guidance (and knowledge) you have been taught?" The scholar knew that Musa would not be able to bear his company and would not be able to be patient with his knowledge, so the scholar said to him: Indeed, you will never be able to have patience with me. "And how can you be patient with something whose reality you do not know?" [Surah al-Kahf: 68] Then Musa (peace be upon him), offering his excuse, said to him: "If Allah wills, you will find me patient, and I will not disobey you in any matter." The scholar knew that Musa would not be patient with his knowledge, so he said: "Then if you follow me, do not ask me about anything until I myself mention it to you." Then the two of them boarded the boat and the scholar tore it open; his tearing of the boat was for the pleasure of Allah, while for Musa (peace be upon him) it was a cause of displeasure. Then they met a boy and he killed him; his killing of him was for the pleasure of Allah. Then the narrator mentioned some of the story and discourse, and (this narration) did not go beyond Ibn Abbas (may Allah be pleased with them both) (that is, it is mawquf). This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Ubayy bin Ka'b (may Allah be pleased with him) that he said that the Messenger of Allah (peace and blessings be upon him) said: "May Allah Almighty have mercy on us and on Musa. (He, peace and blessings be upon him, began the supplication with himself.) Had he been patient, (more of) his news (circumstances) would have been related to us, but he had said: 'If I ask you about anything after this, then do not keep me in your company; you have surely received from me (a final) excuse.' [Surah al-Kahf: 76] " This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it.