Translation:Mother receives a letter from older sister in Japan.
But it's not what the Indonesian sentence says, because there is no -nya ending. Remember that these sentences are included in Duolingo in both directions, so if you add "her" to the English translation, then the Indonesian sentence would have to be changed to a more unnatural one to match the modified English sentence (otherwise, people would complain). Isn't it more imortant that the sentences are more natural-sounding in Indonesian than in English in a course for learning Indonesian?
I recognize the dilemma, but part of the art of translation is making something sound natural in the language into which one is translating. A sentence that is stiffly and woodenly grammatically correct but which still doesn't sound like anything that anybody who really knows the language would ever say would not be a good translation. Good translations also have to sound natural.
English requires a determiner (or article, if you prefer that term -- the, a/an) or a possessive pronoun before "older sister" in order to be a grammatically correct and natural English sentence.
Indeed it sounds better and the most natural interpretation.
As for the supposed dilemma. I'd say sentences need to be grammatically correct in both/all languages/translations and preferably natural as well.
For native as well as non-native speakers it's best to keep using grammatically correct sentences in English.
For literal interpretations it could be useful to add glosses.
In any case this and several other sentences need at least an article like 'an' for being grammatically correct.
I believe kakak is used much the same way as ibu ir bapak, as a title. So the sentence mum recieves a ketter from dad, is grammatically ewuivalent to mum recieves a letter from sister (kakak). Implication's that its my kakak, but because implication is there it doesnt need to be specified. Someone with more cultural knowledge than me can hopefully confirm or refute this.