Prostration of forgetfulness when praying behind an imam

The one who
is praying behind am imam must follow the imam in doing the prostration of
forgetfulness if he prayed all the rak’ahs with him, i.e., if he did not
join the prayer late. That is because of the general meaning of the words of
the Prophet (peace and blessings of Allaah be upon him): “The imam is
only appointed to be followed, so do not differ from him. When he bows, then
bow, when he says ‘Sami’a Allaahu liman hamidah (Allaah hears
the one who praises Him)’ then says ‘Rabbana laka’l-hamd (Our Lord,
to You be praise)’, and when he prostrates, then prostrate.” Narrated by
al-Bukhaari (722) and Muslim (414). 

With regard
to the one who joins the prayer late and has missed one rak’ah or more, he
should follow the imam if he does the prostration of forgetfulness before
the salaam, but he should not follow him if he does it after the salaam
because the one who joins the prayer late cannot say the salaam with the
imam, rather he has to make up what he has missed, then say the salaam, then
do the prostration of forgetfulness, then say the (final) salaam. 

This is in
general terms. As for a more detailed discussion, we can sum up the issue of
the person praying behind an imam and the prostration of forgetfulness as
follows: 

1 – If a
person offers the entire prayer with the imam, then the imam makes a mistake
and does the prostration of forgetfulness, he has to follow him, whether he
does the prostration before the salaam or after.  

2 – If a
person joins the prayer late, and the imam makes a mistake in the part of
the prayer that he catches up with, then it depends: if the imam does the
prostration of forgetfulness before the salaam, the person praying behind
him should prostrate with him, then complete his prayer, then do the
prostration of forgetfulness once again, because the first prostration that
he did with the imam was not at the proper place for him, because the
prostration of forgetfulness cannot be done during the prayer, rather it
should be done at the end of the prayer, so his prostration with the imam
was merely for the purpose of following the imam. 

If the imam
prostrates after the salaam, then the person who joined the prayer late
should not prostrate with him, rather he should stand up and complete his
prayer and say the salaam, then do the prostration of forgetfulness and say
the salaam. 

3 – If the
person praying behind the imam joined the prayer late, and the imam made a
mistake in the part of the prayer that he did not catch up with, such as if
he made a mistake in the first rak’ah and the person joined the prayer in
the second rak’ah: 

If the imam
prostrates before the salaam, the person praying behind him should follow
him, then complete his prayer, but he does not have to prostrate again
because the ruling on his imam’s mistake does not apply to him. 

If the imam
does the prostration after the salaam, the person praying behind him should
not follow him, and he does not have to prostrate after finishing his prayer
either, because the ruling on his imam’s mistake does not apply to him, as
the mistake happened before he joined the imam in the prayer. 

All of these
cases apply when the mistake is made by the imam. If the mistake is made by
the person praying behind the imam, that is also subject to further
discussion: 

4 – If the
person praying behind the imam makes a mistake in his prayer, and he did not
join the prayer late, i.e. he caught up with all the rak’ahs with the imam,
such as if he forgets to say “Subhaana Rabbiy al-‘Azeem (Glory be to
my Lord the Most Great)” when bowing, then he does not have to do the
prostration of forgetfulness, because the imam carries it for him. But if we
assume that the person made a mistake that invalidates one of the rak’ahs,
such as if he forgot to recite al-Faatihah, then in that case he must stand
up when the imam says the salaam and repeat the rak’ah that was invalidated
because of his mistake, then he should recite the tashahhud, say the salaam
and do the prostration of forgetfulness after the salaam. 

5 – If the
person praying behind the imam makes a mistake in his prayer, and he joined
the prayer late, then he should do the prostration of forgetfulness whether
he made the mistake whilst he was praying with the imam or after he stood up
to complete the part of the prayer that he missed, because if he prostrates
he will not be differing from the imam, as the imam will already have
finished his prayer.  

See:
Risaalah fi Ahkaam Sujood al-Sahw by Shaykh Ibn ‘Uthaymeen (may Allaah
have mercy on him) 

And Allaah
knows best.