Does any text/source indicate that Shlomo HaMelech was a prophet?
I ask because according to Muslims he was a prophet.
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The Gemara in Sotah 48b writes:
משמתו נביאים הראשונים מאן נביאים הראשונים אמר רב הונא זה דוד ושמואל ושלמה
§ The mishna taught: From the time when the early prophets died, the Urim VeTummim was nullified. The Gemara poses a question: Who are the early prophets? Rav Huna says: This is referring to David, and Samuel, and Solomon, and after their death the Urim VeTummim was no longer used. (Sefaria translation & notation)
According to the list assembled on jewfaq.org, using the talmudic list (and the commentary on the Talmud), Solomon was a prophet as evidenced as follows:
Solomon II Sam 12:24; 1 Kings 1:10 - 11:43
See Rashi on Megillah 14a, who cites Sefer Halachos Gedolos in the name of Seder Olam, who counts David and Shlomo in the list of the 48 Neviim.
However the Gra in his emendations (ad loc.) takes David and Shlomo out of the count.
See also Zohar (II, 154a) that states that Moshe Rabbeinu was the only person in history to merit both prophecy and monarchy. This would theoretically exclude David and Shlomo.