Is it permissible to substitute a vow with charity given to sanitation workers instead of the school's female staff, due to forgetting and being unable to fulfill it at the present time?

The phrasing "If I pass the exam, I will give charity to the school's female staff" is considered a promise, not a vow (nadhr). It is commendable to fulfill it, especially if the promise is related to obedience to Allah, but its fulfillment is not legally binding. However, if the phrasing is "If I pass the exam, it is a duty upon me for Allah to give charity" or anything that indicates commitment, then it is a vow (nadhr) that must be fulfilled by giving charity to those named "the school's female staff." There is no need to rush the fulfillment unless a specific time has been set for it.