Is it permissible for a Muslim woman to swear upon the Holy Quran that she was unaware of the ruling concerning breastfeeding which prohibits marriage before its completion, in order to prove her right in a divorce case?

The majority of scholars hold that the testimony of the wet nurse alone is insufficient to establish prohibition (of marriage due to fosterage). Those who consider it sufficient stipulate certainty and absence of accusation. There has been a difference of opinion among scholars regarding the number of sucklings that establish prohibition. The resolution of such matters is to be referred to the Sharia (definition) judiciary. As for the oath, it is not permissible for your sister to swear on the Quran that she did not know about the fosterage if she was aware of it before marriage. If she does so, this is a perjured oath (yamin (definition) ghamus), which is one of the gravest sins. A false oath hastens punishment for its swearer in this world before the Hereafter.