Is the rak'ah counted for someone who caught the opening takbeer but delayed their bowing until the imam had already risen from bowing?

If the Imam begins to move to a new pillar, the worshipper should not follow him until the Imam has begun the new pillar. It is not permissible for the worshipper to lag behind his Imam except for a valid excuse.

If he lags behind due to an excuse, he must perform what he missed and then follow his Imam. If the lagging occurred in a complete pillar, he must perform it and then follow his Imam.

If the lagging occurred in a part of a pillar, then if he is certain he will not miss the second rak'ah, he should perform what he missed and follow his Imam. But if he fears missing it, he should abandon what he missed, and his first rak'ah will be nullified; he should then stand to perform a rak'ah after the Imam says the salutation.

If his lagging was for a complete rak'ah or more, he should follow the Imam in what remains and then make up what he missed after the Imam says the salutation.