Is the prayer valid if the worshipper caught the Imam while he was bowing, and said the opening Takbir, then the Imam rose before the worshipper bowed, so the worshipper completed the prayer and said the Taslim, then performed one Rak'ah?

If someone joins the Imam while he is bowing, he should say the takbirat al-ihram (opening takbir) while standing, then descend into bowing. If he doubts whether he caught the bowing, he should cancel that rak'ah (unit of prayer). If he knows that the Imam rose before he could bow, he is not permitted to bow.

If the follower says the salam (concluding salutation) with the Imam, knowing that he still owes a rak'ah, his prayer becomes invalid and he must repeat it, because he deliberately concluded it before completing it. However, if he said the salam out of ignorance or forgetfulness, there is no fault upon him.