Alma 11 - 13

As Amulek begins to talk to the people of his own city Ammonihah, he tells them -

"...I am...a man of no small reputation among all those who know me; yea, and behold, I have many kindreds and friends, and I have also acquired much riches by the hand of my industry.
5 Nevertheless, after all this, I never have known much of the ways of the Lord, and his mysteries and marvelous power." (Book of Mormon Alma 10:4 - 5)

But then he seems to catch himself -

"...I said I never had known much of these things; but behold, I mistake, for I have seen much of his mysteries and his marvelous power; yea, even in the preservation of the lives of this people.
6 Nevertheless, I did harden my heart, for I was called many times and I would not hear; therefore I knew concerning these things, yet I would not know; therefore I went on rebelling against God, in the wickedness of my heart..." (Book of Mormon Alma 10:5 - 6)

I think this may be true for many even in our day in that they don't want to hear, or want to know. They like there lifestyle and choose not listen. But for Amulek, he tells us -

"...As I was journeying to see a very near kindred, behold an angel of the Lord appeared unto me and said: Amulek, return to thine own house, for thou shalt feed a prophet of the Lord; yea, a holy man, who is a chosen man of God...and he is an hungered, and thou shalt receive him into thy house and feed him, and he shall bless thee and thy house; and the blessing of the Lord shall rest upon thee and thy house.
8 And it came to pass that I obeyed the voice of the angel, and returned towards my house. And as I was going thither I found the man whom the angel said unto me...and it was this same man who has been speaking unto you concerning the things of God." (Book of Mormon Alma 10:7 - 8)

The key to Amulek's conversion was that he "obeyed" the voice of the angel. Alma followed in his teaching how important it is to have faith and obey -

"...It is given unto many to know the mysteries of God; nevertheless they are laid under a strict command that they shall not impart only according to the portion of his word which he doth grant unto the children of men, according to the heed and diligence which they give unto him.
10 And therefore, he that will harden his heart, the same receiveth the lesser portion of the word; and he that will not harden his heart, to him is given the greater portion of the word, until it is given unto him to know the mysteries of God until he know them in full." (Book of Mormon Alma 12:9 - 10)

After Amulek received Alma in his home and did feed him as instructed by the angel, we read that -

"...Alma tarried many days with Amulek..." (Book of Mormon Alma 8:27)

I'm sure it was during this period that Amulek did repented and humbled himself giving heed to words of Alma. By the time Amulek is preaching to the people of Ammonihah, he had come to know much of the "mysteries of God" in that he had been given the "greater portion of the word." This becomes apparent with his profound teachings on the atonement and the resurrection of all men. Zeezrom asked Amulek of the Son of God -

"...Shall he save his people in their sins?..." (Book of Mormon Alma 11:34)

To which Amulek said -

"...he shall not, for it is impossible for him to deny his word." (Book of Mormon Alma 11:34)

After Zeezrom challenges his answer, Amulek explains -

"...I say unto you again that he cannot save them in their sins; for I cannot deny his word, and he hath said that no unclean thing can inherit the kingdom of heaven; therefore, how can ye be saved, except ye inherit the kingdom of heaven? Therefore, ye cannot be saved in your sins." (Book of Mormon Alma 11:37)

"And he shall come into the world to redeem his people; and he shall take upon him the transgressions of those who believe on his name; and these are they that shall have eternal life, and salvation cometh to none else.
41 Therefore the wicked remain as though there had been no redemption made, except it be the loosing of the bands of death; for behold, the day cometh that all shall rise from the dead and stand before God, and be judged according to their works." (Book of Mormon Alma 11:40 - 41)

Amulek taught that all will be resurrected in that -

"...The spirit and the body shall be reunited again in its perfect form; both limb and joint shall be restored to its proper frame, even as we now are at this time; and we shall be brought to stand before God, knowing even as we know now, and have a bright recollection of all our guilt.
44 Now, this restoration shall come to all, both old and young, both bond and free, both male and female, both the wicked and the righteous; and even there shall not so much as a hair of their heads be lost; but every thing shall be restored to its perfect frame, as it is now, or in the body, and shall be brought and be arraigned before the bar of Christ the Son, and God the Father, and the Holy Spirit, which is one Eternal God, to be judged according to their works, whether they be good or whether they be evil." (Book of Mormon Alma 11:43 - 44)

Alma concludes with the word of the Lord -

"...Therefore, whosoever repenteth, and hardeneth not his heart, he shall have claim on mercy through mine Only Begotten Son, unto a remission of his sins; and these shall enter into my rest.
35 And whosoever will harden his heart and will do iniquity, behold, I swear in my wrath that he shall not enter into my rest." (Book of Mormon Alma 12:34 - 35)