Does one who catches up with one unit (rak'ah) of the 'Isha' or Fajr prayer receive the reward for praying half a night, or a full night?

Whoever catches one rak'ah of a prayer has caught the prayer. And whoever catches one rak'ah of the Isha and Fajr prayers in congregation, it is as if he stood in prayer the entire night. And whoever catches one rak'ah of the Isha prayer in congregation, it is as if he stood in prayer half the night. And whoever catches one rak'ah of the Fajr prayer in congregation only, the apparent meaning of the narration in Muslim is that he is like one who stood in prayer the entire night. However, it is also said that this is only attained by combining both prayers, because the narration in Muslim is interpreted in light of the narrations by Abu Dawud and Tirmidhi. It is also said that standing in prayer for an entire night is attained by the Subh prayer alone due to the effort required to attend it, as sleep at that time is most enjoyable.