Did King Solomon's mother write Proverbs 31 to her son?

Proverbs 31:1: "The Words of king Lemuel, the prophecy that his mother taught him." King Lemuel is mentioned nowhere else in The Bible, which has left the door open to all kinds of speculation as to the true identity of this king. The signature says that Lemuel wrote this material, not his mother.

The Book of Proverbs is believed to have been written in several successive layers, with the oldest layer dating from the Babylonian Exile. The earliest passages consist of utterances by Lady Wisdom, and other material about her, written when Wisdom began to supercede the ancient goddess Asherah among the Jews. Later passages talk of wisdom in the philosophical sense, obscuring the original message of Wisdom, but apparently without actually removing any Wisdom material. The last of this material is that written by "King Lemuel".

Wisdom entered the belief system of the Jews long after the time of King Solomon, who is not otherwise known to have referred to himself as "Lemuel". This, along with other evidence that causes scholars to date Proverbs after the Babylonian Exile, precludes Solomon or his mother as the author of this chapter.