Translation:My good student has friends in Moscow.
Native speaker here. "у неё есть" - she has, "у него есть" - he has, "у моей хорошей ученицы есть" - my good (female) student has, "у моего хорошего ученика есть" - my good (male) student has. BTW the pronunciation of the word "хорошей" in the audio (at least on my Android SF) is bad - the stress should be on the 2nd "о".
Yes, the stress "хорошЕй" is wrong. The some incorrect word "хорошЕй" (from the words "хорошО" or "хорОшая" or "хорОший" or "хорОшее") has the same meaning as "лУчше" = better. It must be the stress "хорОшей" here because it is Genitive case of the adjective "хорОшая". IMHO. I sent report "The audio does not sound correct".
In Russia there is a set expression "мой хороший друг" that means not simply a friend but a close friend. But we don't have such a set expression "моя хорошая ученица" as not simply a student but a close student. Of course you can say "моя хорошая ученица", there are no mistakes, but the sentence "У моего хорошего друга есть друзья в Москве" most probably implies that I can count on their help ,because they will be my friends, too. And "моя хорошая ученица" just means she studies well, no more. If I talk about her friends then the fact that she is a good is redundant. If I talk that she is good then the redundant thing is her friends in Moscow.