What is her obligation regarding the aid that was deposited into her account despite her request to stop it, knowing the concurrent verification date, and is the amount considered her property?

Your informing the employee is not sufficient to absolve you of responsibility for the amount. Rather, you must refer to the competent official in the concerned entity and inform them of what happened, and that you have found a job. Then, either they will permit you to benefit from the aid or request its return. If they permit you, there is no harm in it, provided that they are authorized to do so. If they request its return, then you are obligated to do so, according to the Almighty's saying: "O you who have believed, fulfill [all] contracts," and the Prophet's (peace be upon him) saying: "Muslims are bound by their conditions."