Types and Shadows of New Covenant in Solomon's Test

 King Solomon’s test with the two mothers and the baby (1 Kings 3:16–28) foreshadows the New Covenant through Christ as the ultimate wise judge, the true mother's self-sacrificial love representing divine grace, and the sword of division exposing human heart motives. [1, 2, 3]

King Solomon as a Type of Christ

Divine Wisdom: Solomon possessed a wisdom from God that surpassed human capability to judge hearts and render true justice (1 Kings 3:28). This reflects Christ, in whom "are hidden all the treasures of wisdom and knowledge" and who judges with perfect spiritual discernment. [1, 2, 3]
The Greater than Solomon: Jesus explicitly presented Himself as the fulfillment and pinnacle of Solomon’s royal wisdom and authority (Matthew 12:42).

The Sword, the Division, and the Two Mothers

The Sword of Truth: Solomon called for a sword to divide the child (1 Kings 3:24), acting as a type of the Word of God, which is "sharper than any two-edged sword, piercing to the division of soul and of spirit" (Hebrews 4:12) and exposing the thoughts and intents of the heart. [1, 2, 3, 4]
The False Claimant (The Old Covenant / Works-based mindset): The woman willing to see the baby cut in two ("let it be neither mine nor yours") mirrors a legalistic or selfish spirit that destroys life for the sake of fairness or self- vindication. [1, 2, 3, 4, 5]
The True Mother (The New Covenant / Grace and Life): The real mother who chose to forfeit her own rights and possession so that the child might live ("give her the living child, and by no means kill him") mirrors the heart of God in the New Covenant—sacrificing position and enduring heartbreak to ensure the preservation of life. [1, 2, 3, 4, 5]

If you would like, I can expand on how Hebrews interprets Old Testament narratives or explore other royal types of Christ in the historical books.