It ought to do just fine for running Win 7 -- but if all she's doing is web browsing, skype and office, you'd probably be better served by just reformatting the drive on the old machine, and reinstalling the OS -- makes everything fresh and snappy, clears out junk, and is much cheaper -- particularly if you'd be going to a new machine anyway.
What I would maybe recommend beyond even that is adding a SSD using the money you'd save from not doing a hardware upgrade. For the low-stress tasks, an SSD can make everything seem much smoother.
What's your reason for upgrading, other than the simple fact of it being 2 years later?