Even though the Torah commands us to wipe out the descendants of Amalek, if an Amalekite agrees to observe the seven Noahide laws, he no longer has the status of an Amalekite, and one may not kill him. The seven Noahide laws are the prohibitions against idolatry, forbidden sexual relations, murder, theft, blasphemy, and eating the limbs of a live animal; and the obligation to set up a court system that will adjudicate all interpersonal disputes justly.
Moreover, even if the Amalekites do not volunteer to observe the seven Noahide laws, we are commanded to offer them peace before waging war against them. That is, we offer them the opportunity to adopt the seven Noahide laws and to agree to be subservient to, and pay tribute to, the Jewish people. If they accept these conditions of peace, we do not wage war against them. If they refuse, however, we fight them until they are eradicated. Even if they reconsider afterward and beg for peace, we do not accept; once the war has begun, we fight them until they are eradicated (mt, Laws of Kings 6:1-4; Kesef Mishneh ad loc.).
The poskim disagree about whether an Amalekite who wants to convert to Judaism may be accepted. Rambam (mt, Laws of Prohibited Sexual Relations 12:17) maintains that an Amalekite may convert. Accordingly, the Sages state that descendants of Haman, who was himself of Amalekite stock, taught Torah in Bnei Brak (Gittin 57b, San. 96b). Thus, our forebears accepted converts from the descendants of Amalek.
Others assert that we do not accept Amalekite converts. This is the view of R. Eliezer, cited in the Mekhilta (end of Parashat Beshalaĥ), who relates that God swore by His Throne of Glory that an Amalekite who comes to convert should not be accepted. According to this position, Haman’s descendants were only allowed to teach Torah in Bnei Brak – as the Sages attest – as the result of an error: A rabbinical court accepted a convert without knowing that he is a descendant of Amalek. Alternatively, an Amalekite descendant of the wicked Haman raped a Jewish woman, and those Torah teachers from Bnei Brak descended from her son, who was considered Jewish (Resisei Laila 38:5).
Others maintain that we do not accept the conversion of Amalekites, interpreting the statement that Haman’s descendants taught Torah in Bnei Brak in various ways. Some explain that the lineage of a non-Jew is determined by the father, and these teachers descended from Haman through a daughter (Mahari Engel, Gilyonei Ha-Shas, Gittin 57b; Maharsham 3:272). Others explain that, le-khatĥila, we do not accept Amalekite converts, but if they are accepted by accident, their conversion is valid (Yeshu’ot Malko, Likutim 15). Others maintain that the conversion is valid only if the mistake is discovered several generations later, but if a convert’s Amalekite origin is revealed immediately, the conversion is invalidated (Shvut Yehuda on the Mekhilta). Others maintain that the teachers descended from an Amalekite who assimilated into another nation and converted afterward. In such a case, it is impossible to know that he is from Amalek, and thus we accept him. Later on, it was revealed through divine inspiration that these teachers were descendants of Haman, but their conversion was still valid (R. Ĥayim Palachi, Einei Kol Ĥai, San. 96b). It is also possible that an Amalekite can divest himself of the status of Amalek by accepting the seven Noahide laws, and then, at a later stage, convert (suggested by Ĥida, Petaĥ Einayim, San. 96b). According to Reponsa Kol Mevaser 2:42, we may accept an Amalekite convert; the Mekhilta only prohibits such a convert from marrying into the Jewish people.