The most significant influence of Amenemope on the Tanakh is found in the book of Proverbs, which copies some of Amenemope verbatim. The Wisdom of Amenemope was lost for over 2400 years, however, in the late 1800s, several copies were found by Egyptologists both on papyrus and tablets. It is not clear when exactly it was lost, but it was no longer in circulation by the time the Septuagint was translated at the Library of Alexandria circa 250 BC, and there is no evidence the Library ever acquired a copy of it.
If the biblical story of Solomon is essentially accurate, then his Egyptian wife would have almost certainly given him a copy of the Wisdom of Amenemope, as it carried the name of her father. This was not the Amenemope that wrote the Wisdom of Amenemope, however, it still would have made a good present to a barbarian king she would no doubt want to Egyptianize. The influence of Solomon's wives over his beliefs is a central aspect of his story within the biblical narrative, with the Levites that wrote the surviving versions of the books of Kingdoms (Samuel and Kings) ultimately describing the downfall of the unified kingdom of Israel (Judea and Samaria) as being because of his actions.
Whether Solomon existed or not, the Book of Proverbs was compiled by someone who ascribed it to him. This person drew on many ancient sources, but clearly had a copy of the Wisdom of Amenemope in his possession. The fact that the author of Proverbs translated texts directly from Amenemope is not in doubt, and almost all major Christian denominations have recognized the preeminence of the Wisdom of Amenemope on the compilation of Proverbs.