What is the ruling on someone who enters the prayer while the imam is bowing, and does not recite Al-Fatihah, or only omits its recitation in the first rak'ah, or leaves the prayer then re-enters it while the imam is bowing?

Whoever prays behind an Imam in a silent prayer and the Imam bows quickly, should follow him in bowing and not wait to recite Al-Fatihah, and his prayer is valid. If he makes the intention to pray and then interrupts his prayer, thinking he did not catch the rak'ah, then he makes the intention to pray a second time and catches his Imam bowing, then he has caught that rak'ah and his prayer is valid, even if he did not recite Al-Fatihah. His exiting the prayer in this case is not prescribed, and there is no sin upon him if he did not do so intentionally. It is not prescribed for a worshipper who was unable to recite Al-Fatihah in the first rak'ah to perform a substitute rak'ah for it, nor to recite the Al-Fatihah he missed in the remaining rak'ahs.