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Solomon reigned from 971 to 931 B.C. and Hezekiah from 715 to 686 B.C.9We do not know when the sages, Agur, or Lemuel lived.
The earliest the Book of Proverbs could have been in its final form was in Hezekiah's day, but it may have reached this stage later than that. We have no way to tell.
The contents of the book could have been in existence in Solomon's lifetime though not assembled into the collection we know as the Book of Proverbs.