Dought & clear, - Should one who joins the prayer late recite the opening du‘aa’?

The opening du'aa' (du'aa' al-istiftaah) should come at the beginning
of the prayer. If I join the congregation at the beginning of the
second rak'ah, for example, should I recite it or have I missed the
time for it? In other words, should the opening du'aa' be recited only
in the first rak'ah, and after that should it not be recited? Or is it
that whenever the worshipper starts his prayer, he should say it even
if he did not say it in the first rak'ah?
Praise be to Allah.
The opening du'aa' is Sunnah according to the majority of scholars,
and whenever the worshipper catches up with his imam in the first or
second rak'ah, he should recite the opening du'aa', so long as he is
not worried that the imam will bow (too soon). But if he is worried
that the imam will bow, then he should recite al-Faatihah only,
because reciting it is obligatory.
An-Nawawi (may Allah have mercy on him) said: If one who joins the
prayer late starts to pray, then the imam says Ameen immediately after
he has started to pray, then he should say Ameen and then recite the
opening du'aa', because the saying ameen is brief. If the one who
joins the prayer late catches up with the imam in the final tashahhud,
he should say takbeer and sit down, then if the imam says the salaam
as soon as he has sat down, then he should stand up (to make up what
he has missed of the prayer) and not say the opening du'aa', because
he has missed the place for it.
End quote fromal-Majmoo', 3/275
He also said: If he catches up with him when he is still standing, and
he knows that he will be able to recite the opening du'aa' and seek
refuge with Allah and recite al-Faatihah, then he must do so. This was
stated by ash-Shaafa'i inal-Umm, and also by our companions. … If he
knows that he will only be able to recite part of the opening du'aa'
and seek refuge with Allah and recite al-Faatihah, and he will not be
able to do all of it, he should do what he is able to do. This was
stated inal-Umm.
End quote fromal-Majmoo', 3/276
Shaykh 'Abd al-'Azeez (may Allah have mercy on him) said:
If the latecomer joins the prayer when the imam is reaching the end of
his recitation, before bowing, should he start his prayer with the
opening du'aa', or should he join the imam and remain silent?
He replied:
If the latecomer arrives when the imam is bowing, he should bow with
him, and not recite the opening du'aa' or recite any Qur'an; rather he
should say takbeer and bow. But if he comes when the imam is still
standing and there is plenty of time, then he should recite the
opening du'aa' and al-Faatihah. This is what is prescribed for him: to
recite the opening du'aa' and then al-Faatihah, even in the prayers in
which the imam recites out loud. If there is a pause where the imam
falls silent, he should recite it at that time; otherwise he should
recite it to himself, then after that he should listen attentively to
the imam. But if he comes late, when the imam is bowing, then he
should say takbeer and bow, and the requirement to recite al-Faatihah
is waived in this case, because he is excused.
End quote fromMajmoo' al-Fataawa, 30/150
And Allah knows best.