Is it a sin to dispose of the deceased mother's salary—which continued to be disbursed after her death, having been deducted from her during her employment—without the knowledge of the siblings, especially given that none of the siblings are in dire need of that money?

If the condition under which the salary was disbursed is terminated by the mother's death, then the children do not have the right to claim it. The relevant authority must be informed of the death; otherwise, it would be an unlawful appropriation of people's money, and the amounts disbursed after the death must be returned.

If the amount disbursed to your mother exhausted all that was deducted from her, then you have no right. However, if there remains anything from her deducted funds, you are entitled to it, and it is an inheritance to be divided among the heirs according to each one's legal share.