Are the salaries disbursed retroactively from the date of application for the job, and not from the actual start date of work, considered permissible or impermissible?

It is not permissible to take undeserved salaries unless the responsible authority is informed and the error is clarified to them. If they permit its use and the law allows it, then there is no harm. Otherwise, it must be returned, for the Prophet, peace and blessings be upon him, said: “Indeed, some people delve into Allah’s property without right, and for them is the Hellfire on the Day of Resurrection.”