Is the prayer of one who joins the congregational prayer late considered invalid if the Imam prolongs the recitation of the Basmala to the extent that the latecomer is able to recite Al-Fatiha and a short surah in the first two rak'ahs (which are the third and fourth for the Imam), and then the latecomer completes his prayer by reciting only Al-Fatiha in the last two rak'ahs?

It is permissible for the latecomer (masbuq) to recite a Surah (definition) in the rak'ah he joins with the Imam, and his prayer is not invalidated by that. In fact, it would not be invalidated even if he recited it in all rak'ahs. If the latecomer recites it in the rak'ahs he joins with the Imam, he does not repeat it in the remainder of the prayer, according to the view that recitation is specific to the first two rak'ahs. However, according to the view that it is recommended to recite a Surah in all parts of the prayer, then he recites a Surah in all of them. If the latecomer does not recite it in the rak'ahs he joins with the Imam, then he recites it along with Al-Fatihah in the remainder of the prayer, by agreement of the majority of scholars.