duolingo propagating bad grammar, ‘I have more money than him’
the correct phrasing is, ‘I have more money than he (does)’. this is a comparison between two SUBJECTS (apologies for shouting) and therefor requires subject/nominative pronouns. the direct object pronoun ‘him’ is absolutely incorrect.
"John is taller than me" and "John is taller than I" are both correct. However, lots of your readers are likely to think that "John is taller than me" is wrong (even though it sounds natural), and a fair proportion of your readers are likely to think that "John is taller than I" sounds pretentious.
Here "than he" definitely sounds pretentious, maybe even aristocratic :)