Exode 17:14

And the Lord said unto Mosheh, Write this memorial in the book of the elders that were of old, and these words in the hearing, of Jehoshua, that blotting, I will blot out the memory of Amalek from under the heavens.

WRITE THIS FOR A MEMORIAL IN THE BOOK. Rabbi Abraham ibn Ezra commented that “this was a known book, namely, the book of the wars of the Eternal, which contained the history of the wars which G-d fought for those that fear Him, and it is possible that the history began from the time of Abraham.” There is nothing in these words of his but an opportunity [to say something without due consideration].), Ramban agrees with Ibn Ezra’s comment, by way of the plain meaning of Scripture. This is because it distinctly says there, the book of the wars of the Eternal. Here, however, it just says in the book. Hence Ramban rejects Ibn Ezra’s interpretation that here too it refers to that book of the wars of the Eternal, which is no longer extant, and he proposes his own interpretation, as explained in the text.
The correct interpretation appears to me to be that the word, baseifer (in the book), alludes to the Book of the Law, something like that which is written, Take this Book of the Law. He is thus stating: “Write this in the Book of My Law so that the children of Israel should remember what Amalek did, for I will utterly blot out his remembrance, and I will lay My vengeance upon him by the hand of My people Israel.” This is the commandment we find written in the Book of Deuteronomy: Remember what Amalek did unto thee. He said, and rehearse it in the ears of Joshua, to command him to remind Israel of all the travail that had come upon them because of Amalek, for he [Joshua] knows and is witness. G-d is thus hinting that after the conquest of the Land, they would blot out Amalek, for the first commandment upon them was to destroy the seven nations and take possession of the Land. This is Scripture’s intent in what is said there: And it shall be when the Eternal thy G-d hath given thee rest from all thine enemies… that thou shalt blot out the remembrance of Amalek., 25:19. Now had it been like this in the days of Joshua the son of Nun, he would have urged them on to blot out Amalek, but in his days, a good deal of the Land remained to be possessed, and the time for the fulfilling of the commandment did not come until the reign of Saul.

באזני יהושע, that he shall prevail over them when he will be king and keep My commandment to wipe out the name of Amalek.

כתוב זאת זכרון בספר, a reference to the portion in Deuteronomy 25,17-19.

ושים באזני יהושע, make sure that Joshua remembers all this. Moses carried out this command by building the altar and offering up the prayer declaring G’d as his flag.

מחה אמחה את זכר עמלק, not only the people but even their livestock. We know this from the instructions given by the prophet Samuel to King Sha-ul in Samuel 15,3 where the king is ordered to destroy utterly all the possessions of Amalek.

כי מחה אמחה, “for I will completely wipe out, etc.” the repetition of the verb is to tell us that both in this world and in the world to come there will eventually remain no descendants of Amalek.

את זכר עמלק, the word זכר is a reference to Haman, the word Amalek is to be understood at face value.