How should the salary be divided between two sisters after one of them worked in the place of the other with the employer's approval, given their similar financial circumstances?

The determination of the wage is based on what you both agree upon, whether it is equal to, less than, or more than the salary. However, if your sister completes the month in your place without a prior agreement on the wage, then she is entitled to a fair wage (اجر المثل). This is based on Al-Qarafi's statement: "Whoever performs a deed or delivers a benefit to another... if he is volunteering, he does not receive compensation for it, but if he is not volunteering and it is a benefit, then he is entitled to a fair wage for it." And in "Durar al-Hukkam": "If someone instructs another to perform a task for him, and does not mention the wage for his work, and the person performing the work is someone who normally charges for such work, then he is entitled to receive a fair wage, whatever it may be."