ANSWER:

No, you must not make up that rakah. 

You are exempted from reciting fateha and this rakah is valid if you caught the imam in ruku and you got to say the prescribed dhikr at least once. 

During prayer, when the imaam finishes surah and is about to go to ruku and i join him at that part without me Reciting surah fatiha and goes to ruku as well. Should i make up for the rakah at the end since i dint recite surah fatiha ?

Prayer |