Is the wage received for the month of September lawful, knowing that the actual start of work was in October, and if it is not lawful, what is the solution for returning the excess salary?

A salary paid without work is one of two cases: either it was intentional, in which case it is a gift and permissible to benefit from it, or it was a mistake, in which case it must be returned to the granting entity, ensuring that it is redeposited into the treasury or account. The true nature of the salary must be ascertained from the granting entity before disposing of it.