Is it correct? I was taught that it is not correct, but you will still hear it frequently. The rule I learned is to include the verb, then use the same pronoun, e.g.,
I swear that I am much more beautiful than her. she is.==> I swear that I am much more beautiful than she.
Having looked online, it seems like the "rules" may be changing:
https://ell.stackexchange.com/questions/30930/than-her-versus-than-she
https://www.grammar-monster.com/lessons/than_I_me_than_he_him.htm