Is it permissible for a divorced woman to save a portion of the money her sister gives her monthly for her children without her sister's knowledge? And would she be considered sinful or a thief if she does not inform her sister of this?

The questioner informed her sister that she is saving some money for her children. It is permissible for her to save, and she is not obliged to inform her sister of the exact amount she is saving as long as her sister has not asked her. However, if the sister increased the expenditure due to a certain assumption on the part of the questioner, and this assumption has now been dispelled, then it is not permissible for her to take the increase unless she informs her sister of the true situation. This is based on the statement of Ibn Hajar Al-Haytami and Al-Barmawi Al-Shafi'i: "If someone is given something because the giver assumes a certain quality in them, but in reality, it is otherwise, and had the giver known, they would not have given, then the recipient does not own what they take."