Well `apparently`HPFSCHED.EXE is a background task which is installed by the drivers of some HP DeskJet printers (e.g. 660C, 670C, 680C, 690C, 720C). Its sole purpose is to remind you from time to time to clean the cartridges in your DeskJet so as to keep the print quality high. Most end-users find these popups extremely irritating and in that respect Epson have found a better compromise by implementing the cleaning of cartridges as an automatic hardware feature which kicks in at specific intervals of usage, as well as being something you can start manually.
It`s suggested that any printer software is uninstalled and reinstalled again.
Don`t know whether it`s totally right or not hun, I`m hoping someone else may have some info for you but i`ll keep looking.