Praise be to Allah, the Lord of the Worlds.
For valid combination of two prayers under the excuse of rain, it is conditioned for the late comer to join the congregation during the second prayer, be it at its beginning or end, because what counts, here, is catching any part of the second prayer. The evidence on that condition is that it was confirmed that the Prophet (PBUH) had done so whenever two prayers were joined because of rain. Later, scholars have done their own Ijtihad and arrived at the conclusion that it suffices that the late comer catches any part of the second prayer with the congregation. However, scholars have disagreed about some details in that regard.
Al-Shabramalsi, a Shafie scholar, said: "It isn`t conditioned that the one who came late to the prayer should have joined the congregation in the first prayer. Rather, it suffices that he manages to join the congregation at any part of the second prayer." {Hashyat Nehayat al-Mohtaj, vol.2/pp. 281}. In conclusion, the above person`s prayers and combination are valid, and it will avail him Insha`allah. And Allah Knows Best.