Praise be to Allah.
The scholars differed as to whether breast-feeding can be proven by the testimony of one woman. The majority are of the view that breast-feeding cannot be proven by the testimony of one woman, and they differed concerning the number required to prove breast-feeding.
The Hanbalis are of the view that breast-feeding can be proven by the testimony of one woman. They quoted as evidence for that the report narrated by al-Bukhaari (5105) from ‘Uqbah ibn al-Haarith (may Allah be pleased with him) who said: I married a woman, then a black woman came to us and said: I breast-fed both of you. I went to the Prophet (blessings and peace of Allah be upon him) and said: I married So and so, daughter of So and so, and a black woman came to us and said to me: I breast-fed both of you, and she is lying. He turned away from me, so I came to him from the other side and said: She is lying. He said: “How could you keep her as your wife when that woman has said that she breast-fed you both? Leave her (i.e., divorce your wife).”
The more correct view is that of the Hanbalis, that breast-feeding may be proven by the testimony of one woman, because of the hadeeth quoted above, on condition that she be of good character and there are no reservations about her testimony.
Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (8/153): If one woman testifies to breast-feeding, then marriage [of the two who were breast-fed by the same woman] is haraam, if she is of good character. End quote.
Al-Bahooti (may Allah have mercy on him) said in Kashf al-Qinaa‘ (5/457): If one woman who is of good character testifies that she breast-fed him five times within the first two years, or a woman of good character testifies that So and so breast-fed him five times within the first two years, or one man testifies to that, then breast-feeding is proven thereby and there is no need for an oath to be sworn by the one concerning whom testimony was given or by the woman who witnessed it, because of the report of ‘Uqbah ibn al-Haarith (may Allah be pleased with him) who said: I married Umm Yahya bint Abi Ihaab, then a black slave woman came and said: I breast-fed both of you. I went to the Prophet (blessings and peace of Allah be upon him) and told him about that, and he said: “How can you (marry her) when she has said that?” And he forbade him to marry her. According to another report he said: “Leave her (i.e., divorce your wife).” Narrated by al-Bukhaari… And the testimony of a woman who is not of good character is not to be accepted. End quote.
Based on what is mentioned above, that the view of the Hanbalis is most likely to be correct, with regard to this woman who is well known for lying, her word is not to be accepted when she claimed that she breast-fed that girl, because she is not trustworthy.
But we also advise you to be cautious in such matters and to look at the circumstantial evidence. If it is possible that what she says could be true, such as if she had a baby around the time when she claims that she was breast-feeding, and such things were common among you (i.e., women breast-feeding one another's babies), then to be on the safe side, not going ahead with this proposal is a good idea, especially as it is the matter of a proposal, and if the man does not go ahead with it without giving a reason, he is not doing anything concerning which there are shar‘i reservations, and there will be not be any trouble or problems.
But if it is the matter of annulling a marriage contract that has already gone ahead, then it should not be annulled on the word of someone like this woman.
And Allah knows best.