Sheikh Muhammad b. Sâlih al-`Uthaymîn
If the worshipper joins the congregation late, while the imam is still standing, he should enter into his prayer with the initial takbîr (takbîrah al-ihrâm) then proceed to offer the opening supplication (du`â’ al-istiftâh). He should then commence with reciting Sûrah al-Fâtihah if there is still time, and read as much of it as he can.
If there is enough time for him to recite Sûrah al-Fâtihah in full before the imam bows, well and good.
If not, he will be exempted from reading it, since he did not get a chance to do so before the imam bowed.
He should not try to finish reciting Sûrah al-Fâtihah after the imam has bowed. Instead, he should follow the imam and bow as well. In doing so, he will be carrying out his prayer in the proper order according to what is required of him.
And Allah knows best.
Source: Islam Today