Praise be to Allah.
Yes, whatever the person who joins the prayer late catches up with, with the imaam is the first part of his prayer. See Question no. 23426.
And it is mustahabb to raise the hands when getting up after the first Tashahhud.
But does the person who is one rak’ah behind the imam have to raise his hands when getting up after saying the Tashahhud or not?
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about that and he said:
He should raise his hands, because it seems that the hands should be raised when he gets up for the third rak’ah because he is getting up after reciting the Tashahhud, and this applies to the one who joins the prayer with the imam late. And Allaah knows best.
The questioner’s comment that raising the hands is obligatory is not correct, because raising the hands (at this point) is one of the Sunnahs of prayer, and is not obligatory (waajib).