Heidegger's Bible Handbook: Proverbs: Authorship
2. The wisdom of Solomon. He was the author of the Proverbs, not the collector. Who was Agur and Lemuel?
Now, these Proverbs are attributed to Solomon, the Son of David, Proverbs 1:1. In answer to whose prayer, God gave a wise and understanding heart, so that there was none like to him before him, or after him, 1 Kings 3:12. Whence he is said to have spoken three thousand proverbs, and שִׁירוֹ, his songs, were a thousand and five, 1 King 4:32, where is found an especially luminous description of his wisdom, both spiritual and moral, and natural, both of plants from the cedar in Lebanon to hyssop, and of animals, etc. Therefore, he, inspired by the Holy Spirit, with his own mouth, and hand or pen, celebrated, ennobled, and published the same. Neither is it to be received that this book is an ἐκλογὴν/selection of the best sentences of a great number of writers, who lived before Solomon; which sort of Compilations many of the Emperors of Constantinople commanded to be written for their use, as Grotius thinks. Certainly, that he himself was the Author, not the Collector, is argued by the title, and by the fact that the Collecting men of Hezekiah, of which sort perhaps were Eliakim, Shebna, Joah, mentioned in 2 Kings 18:26, are said to have selected certain Proverbs of Solomon, Proverbs 25:1. But, that in Proverbs 30 the words of Agur are mentioned, and in Proverbs 31 the words of Lemuel, does not at all hinder the attribution of the same words or Proverbs to Solomon also. For, whether those words, אָגוּר/Agur, which denotes one recovered/collected, penitent, and לְמוּאֵל/Lemuel, which means to God, are appellative, certainly they are attributed to no one more rightly than to Solomon himself: or they are proper, and so applicable to men other than Solomon, those were to be reckoned, not so much others of the words that they committed to writing, as collectors of the ancient words of Solomon.
Dr. Dilday's Lecture: "Proverbs, Part 1"