Is the money the sister received considered permissible or impermissible, given that she did not work that month and the salary was disbursed to her openly and officially?

There is no harm for your sister in taking the salary and benefiting from it if the official is authorized to disburse it despite her absence. However, if he is not authorized, then it is not permissible for her to take the money, because it is public money taken without a legitimate right. The fact that the matter is public or that she did not request the disbursement is not a valid justification.