This is a disputed point in English, turning on whether "than" is acting as a conjunction or preposition. Both sides have many advocates. So "her" or "she" are both accepted, and "she is" sounds less formal than just plain "she". But ending a sentence or clause with a contraction just seems wrong. I've never come across it before that I can recall.
"He is older than she's" is incorrect, while "He is older than she" and "He is older than she is" are both correct and should be accepted.
As far as I know, the answer I gave "He's older than she" is grammatical. Now, I have my doubts about the second contraction in the correction I was given: "He's older than she's"(!?).