Praise be to Allah.
The majority of scholars think that the woman’s milk that has consequences does not necessarily have to result from intercourse with her husband (and resulting pregnancy) or from giving birth; rather if she takes something to stimulate milk production then breastfeeds a child with that, this infant will become her son through breastfeeding. Hence they did not rule it out if a woman who is a virgin who has never been married before breastfeeds a child; she becomes a mother through breastfeeding. This is the view of Maalik, ash-Shaafa‘i and Abu Haneefah, and was regarded as more correct by the Hanbali scholars al-Mardaawi and Ibn Qudaamah.
In order for him to become a son of the woman who breastfeeds him, it is stipulated that she should breastfeed him five times, and that should be when the child is two years old or younger.
Muhammad al-‘Utbi al-Maaliki (may Allah have mercy on him) said: And I heard him –i.e., Imam Maalik – when he was asked about a woman who takes herbs that stimulate milk production, then she breastfeeds with it: does this breastfeeding create the mahram relationship? He said: Yes, that creates the mahram relationship; is it not milk? He said: Yes. He [Imam Maalik] said: Then the mahram relationship is established by that.
Muhammad ibn Rushd al-Maaliki (may Allah have mercy on him) commented on that:
His comment -- that if the woman stimulates the production of milk by something that she takes then breastfeeds with that milk, then it is milk that creates the mahram relationship -- is like what is said in al-Mudawwanah: The milk of a virgin girl creates the mahram relationship; the milk of a woman creates the mahram relationship in all cases, based on the apparent meaning of the words of Allah (interpretation of the meaning): “Forbidden to you (for marriage) are: … your foster mother who gave you suck, your foster milk suckling sisters,” [an-Nisa’ 4:23]. It does not specifically mention a woman who has a husband to the exclusion of one who does not have a husband.
End quote from al-Bayaan wa’t-Tahseel by Ibn Rushd al-Maaliki, 5/153
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said: The words “and one who is not pregnant” mean: if a woman breastfeeds a child without having been pregnant. This happens a great deal: if a child cries, a woman comes along who has no milk and is not married, and she gives him her breast in order to quieten him, and the sucking stimulates milk production. If he breastfeeds five times or more, does he become a son to her? The author said no, because that came about without there having been a pregnancy. But this reason is not sufficient to prove his point. The correct view, which is held by the three imams, is that it does create the mahram relationship; if the child breastfeeds from a woman five times, then he becomes a son to her, whether she was a virgin or beyond the age of childbearing or had a husband. The evidence that it established the mahram relationship is based on the text and rational evidence.
The textual evidence for that is the general meaning of the words of Allah (interpretation of the meaning): “Forbidden to you (for marriage) are: … your foster mother who gave you suck…” [an-Nisa’ 4:23]. And there is nothing in the Qur’aan or Sunnah to stipulate that the milk should be the result of pregnancy, so the general meaning of the text still stands.
The rational evidence is that the wisdom behind the milk establishing the mahram relationship is the nourishment of the child thereby. If the child is nourished by it, then the reason for it creating the mahram relationship has been established. With regard to the verse (interpretation of the meaning) “The mothers shall give suck to their children…” [al-Baqarah 2:233], what it refers to what the mother should do of completing the term of breastfeeding. So the correct view is that a woman’s milk creates the mahram relationship whether it is the result of pregnancy or otherwise. So the milk of a virgin creates the mahram relationship, and the milk of an old woman who has no husband and is past the age of childbearing creates the mahram relationship.
End quote from ash-Sharh al-Mumti‘ ‘ala Zaad al-Mustaqni‘, 13/440, 441
See also the answer to question no. 118709.
Based on that, if a woman takes medicine or eats beneficial foods that do not cause harm and that stimulate milk production, then she breastfeeds a child with it five times and the child is two years old or younger, then he becomes a son to her through breastfeeding and the breastfeeding establishes the mahram relationship which makes marriage haraam and makes it permissible to be alone together or to look at one another and to be a mahram in the case of travel. But it does not establish ties of lineage or obligations of maintenance, or rights of inheritance.
It should be noted that the husband of the woman who breastfeeds in this case will not become a father through breastfeeding, because the milk did not come from him, so it is permissible for his sons from a wife other than the one who is breastfeeding to marry the daughter who was breastfed by that wife and it is permissible for his daughters from a wife other than the one who is breastfeeding to marry the son who was breastfed by that wife.
In al-Fataawa al-Hindiyyah, by a group of Hanafi scholars (1/343) it says: A man married a woman who never bore him any children, then she produced milk and she breastfed a boy. The breastfeeding was from the woman without her husband being connected to it, so the children of this man from any other wife did not become mahrams to the boy. End quote.
In Mughni al-Muhtaaj by ash-Sharbeeni ash-Shaafa‘i (3/420) it says: If a virgin produces milk and she gets married and gets pregnant from her husband, the milk belongs to her and not to the husband so long as she has not given birth, and if she breastfeeds an infant, then her husband is not a father to that child. But if she gives birth to his child, the milk after she gives birth belongs to him. End quote.
The ruling will never differ concerning the husband of the breastfeeding woman with regard to practical shar‘i rulings having to do with looking or being alone with (the one who was breastfed). He is the husband of the mother of the breastfeeding child; if the one who is breastfed is female, then she becomes his stepdaughter and it is haraam for him to marry her and the same rulings apply to him as to a father through breastfeeding in this regard.
It should also be noted that the word “adoption” mentioned in the question is not used in the sense that is forbidden in Islam, which is when the child is attributed to someone other than his real father. Rather what is meant is taking care of an orphan and looking after him. Hence we prefer not using this word in this sense because of the confusion it may create.
And Allah knows best.