Is it permissible to continue receiving the deceased father's salary in exchange for managing his trade, or should each of the children receive a separate wage for their work, and is it permissible for the brother to receive a wage for monitoring the work remotely?

There is no objection to a person being both a partner and an employee at the same time. He is entitled to a percentage of the profit by virtue of the partnership, and a known salary by virtue of his work exceeding that of his partners, if this is agreed upon with them. If one of the partners dies, the partnership is dissolved according to the majority of jurists. His heirs may take his place if they agree with the remaining partners. It is not permissible for the questioner and her brother to take a salary for managing the project unless the other partners agree, and the amount of the salary and its distribution should be according to the agreement. As for what was previously taken, a settlement should be reached for it; otherwise, they are entitled to the wage of similar work, as determined by experts, as long as they were not voluntarily performing the work.