What is the ruling on one who says "Allahu Akbar" to the Imam after he has straightened up (from bowing) in the third rak'ah, and what is incumbent upon him?

The majority of scholars hold that it is recommended for the worshipper, whether an Imam or otherwise, to begin the takbir of transition (takbir al-intiqal) as soon as the transition itself begins. An exception is made for the follower (ma'mum), who follows his Imam. There is no difference in this regard between transitioning from the first tashahhud or any other transition. The Malikis, however, hold that it is recommended to delay the takbir of transition when rising from the first tashahhud. The opinion of the majority is supported by the apparent meaning of the hadith. And whoever acts according to the Maliki school, there is no harm upon him, and the Imam should not prevent the follower from saying the takbir before him.

In the Sahihayn, it is narrated from Abu Hurairah: "When the Messenger of Allah (peace be upon him) stood for prayer, he would say the takbir when he stood, then he would say the takbir when he bowed..." (the hadith).

Al-Nawawi said in his commentary on Sahih Muslim: "One should begin the takbir for rising from the first tashahhud when one begins the transition and extend it until one stands upright. This is our school of thought and the school of all scholars, except for what was narrated from Umar ibn Abd al-Aziz (may Allah be pleased with him), and Malik also held this view, that one does not say the takbir for rising from the two rak'ahs until one is fully standing. The evidence for the majority is the apparent meaning of the hadith."

Ibn Qudamah said in Al-Mughni: "It is recommended that the beginning of his takbir coincides with the beginning of raising his head from prostration, and its end coincides with his standing upright, so that the entire prescribed pillar is encompassed by the takbir. And this applies to the rest of the takbirs, except for one who sits for the short rest (jalsat al-istiraha), for his takbir ends when his sitting ends, then he rises to stand without takbir."