"Thus Josiah, from his earliest manhood, had endeavored to take advantage of his position as king to exalt the principles of God's holy law. And now, while Shaphan the scribe was reading to him out of the book of the law, the king discerned in this volume a treasure of knowledge, a powerful ally, in the work of reform he so much desired to see wrought in the land. He resolved to walk in the light of its counsels, and also to do all in his power to acquaint his people with its teachings and to lead them, if possible, to cultivate reverence and love for the law of heaven. PK 398.1"
"And it came to pass, when the king had heard the words of the book of the law, that he rent his clothes."
Both passages describe Josiah's reaction to the book of the law. The Bible states he rent his clothes, while EGW elaborates on his understanding and resolve to reform based on what he heard.
"And it shall be, when he sitteth upon the throne of his kingdom, that he shall write him a copy of this law in a book out of that which is before the priests the Levites: And it shall be with him, and he shall read therein all the days of his life: that he may learn to fear the Lord his God, to keep all the words of this law and these statutes, to do them:"
Deuteronomy 17:18-19 outlines the king's duty to study the law. EGW's passage describes Josiah fulfilling this principle by resolving to walk in the light of the law's counsels and acquaint his people with its teachings.
"The gravity of the situation and the respect in which he held the prophetess led him to choose as his messengers to her the first men of the kingdom. “Go ye,” he bade them, “inquire of the Lord for me, and for the people, and for all Judah, concerning the words of this book that is found: for great is the wrath of the Lord that is kindled against us, because our fathers have not hearkened unto the words of this book, to do according unto all that which is written concerning us.” 2 Kings 22:13 . PK 398.4"
"Go, enquire of the Lord for me, and for them that are left in Israel and in Judah, concerning the words of the book that is found: for great is the wrath of the Lord that is poured out upon us, because our fathers have not kept the word of the Lord, to do after all that is written in this book."
The EGW passage directly quotes 2 Kings 22:13.
"Go ye, enquire of the Lord for me, and for the people, and for all Judah, concerning the words of this book that is found: for great is the wrath of the Lord that is kindled against us, because our fathers have not hearkened unto the words of this book, to do according unto all that which is written concerning us."
Ellen White directly references 2 Kings 22:13 in this passage.