If a person does not do the obligatory prostration of forgetfulness

If a worshipper deliberately omitted the prostration of
forgetfulness for omitting an obligatory part of the prayer, then his prayer
is invalid, just as if he deliberately omitted any obligatory part of the
prayer. 

But if he forgot to do the prostration of forgetfulness, if
he remembers it after saying the salaam he should do it, unless a long time
has passed or he has left the mosque, in which case he does not have to do
anything, and his prayer is valid. 

Shaykh Ibn ‘Uthaymeen was asked about a man who forgot the
first tashahhud, and he knew that he had to do the prostration of
forgetfulness before the salaam, but he forgot and said the salaam. What is
the ruling? 

He replied: If he remembers within a short time, he should do
the prostration, but if a long time has passed, then it is waived, such as
if he did not remember until after a long time, if he had left the mosque
then he does not have to go back to the mosque, and it is waived in his
case. End quote. 

Fataawa Ibn ‘Uthaymeen (14/50). 

If the imam forgets to do the prostration of forgetfulness,
the person praying behind him should not do it on his own. Rather he should
say the salaam with the imam, then remind him after the salaam to do the
prostration of forgetfulness, then the imam should prostrate and the person
praying behind him should prostrate too. 

And Allaah knows best.