I am prettier than her.
I am prettier than she is.
Comparative adjectives: using than
We use than when we mention the second person or thing in the comparison. If the second person mentioned takes the form of a personal pronoun, we normally use the object form of the pronoun (me, you, him, her, us, them):
Could you carry this? You’re stronger than me.
Not: You’re stronger than I.
Why did you choose Robert? Marie is more experienced than him.
In more formal situations, instead of than + object pronoun, we can use than + subject pronoun + be:
You managed to answer the ten questions correctly? Well, you’re definitely cleverer than I am!
I preferred Henrietta to Dennis. She was always more sociable than he was.
The comparative form is used for comparing two people or things:
He is taller than me.
I don't deny that this is a common colloquial usage, but it is non-standard and not considered formally correct. As your own reference states:
this grammar reference provides hundreds of clear grammar explanations with authentic examples of the way in which the grammar is used in real-life situations, including standard and non-standard varieties of English.
In cases where there are transitive verbs involved, rather than simply adjectives, the colloquial use of objective pronouns instead of subjective pronouns can be downright ambiguous: 'he loves her more than me' has an entirely different meaning to 'he loves her more than I'.
No-one is suggesting that the common colloquial form should not be accepted; merely that the formally-correct version be accepted, too. Repeating the verb 'to be' or an auxiliary after a nominative pronoun is not necessary as it is already implied by the case. 'You’re stronger than I' is perfectly correct; no doubt 'English Grammar Today' (a very basic guide for non-native speakers) is trying not to confuse learners with a less-common alternative, but DL does not suffer from this limitation, as no-one who doesn't input it will see it.
I agree totally with you. The full sentence would be "She is prettier than I am." Just because most people use me does not make it correct, only most used. It is similar to the use of "lay" in "I lay on the bed." Most people say that in the US, but it should be "I lie on the bed." As I have noted elsewhere, in the French Duolingo, Duolingo does accept use of "I" in a sentence such as "She is prettier than I." I don't understand why Duolingo does not accept it in Indonesian. I have pointed this out to Duolingo.
Here is a screenshot of one the lists of correct answers from The Blue Book of Grammar and Punctuation (pub. 2014) with an example of this usage. (I'm posting it as an image in case Google randomly withholds that page from you.)
Edit: image file is here if this is too small to read.
FYI , as I already mentioned earlier :
"I am prettier than him." ==> This is one of the accepted translations.
"I am prettier than he is. " ==> This is one of the accepted translations.
"I am prettier than he ." ==> This is rejected, just as it is rejected by the dictionaries. ( see links above. )
Just click on the link and read for yourself.
I've already posted links to two different dictionaries.
Please post a link to an authoritative source to back up your claim.
(Merriam-Webster, Cambridge, Chambers, or another dictionary).
It would be nice to see several dictionaries contradicting each other.