A person who joined the prayer late forgot to recite the first tashahhud

There are
two issues connected to this question. 

1 – Should
the one who joined the prayer late do the prostration of forgetfulness if he
forgets something in his prayer? 

Al-Bahooti
said in Sharh Muntaha al-Iraadaat (1/232): 

He (i.e.,
the one who joined the prayer late) should also do the prostration of
forgetfulness in the following situations: 

-He should do the prostration of
forgetfulness with regad to the part of the prayer that he did with his
imam, even if he left the imam after that f or a reason.

-The one who joined the prayer
late should also do the prostration of forgetfulness if he forgets something
in the part of the prayer that he offers alone, which is what he makes up
after the imam has said the salaam, even if he prostrated with him because
of his (the imam’s) mistake, because now he is praying alone. End quote.

Shaykh Ibn
Baaz (may Allaah have mercy on him) said: 

As for the
one who joined the prayer late, he should do the prostration of
forgetfulness if he made a mistake with his imam, or if he made a mistake in
the part of the prayer that he offers alone after the imam has finished it.
End quote. 

Fataawa
Ibn Baaz, 11/268. 

It says in
Fataawa al-Lajnah al-Daa’imah (7/151): 

If a person
forgets something whilst making up the part of the prayer that he missed, or
he is not sure about his prayer, then he should act on the basis of what is
certain – which is the lower number – and complete his prayer, then do the
prostration of forgetfulness. End quote. 

2 – When
should the prostration of forgetfulness be done – before the salaam or
after? 

The Sunnah
is that if a person forgets the first tashahhud, he should do the
prostration of forgetfulness before the tasleem. 

Al-Bukhaari
(1224) and Muslim (570) narrated that ‘Abd-Allaah ibn Buhaynah said: The
Messenger of Allaah (peace and blessings of Allaah be upon him) led us
in praying two rak’ahs of prayer, then he stood up and did not sit, and the
people stood up with him. When he had finished praying and we were waiting
for his tasleem, he said takbeer and prostrated twice whilst he was sitting,
before the tasleem, then he said the tasleem. 

This hadeeth
indicates that the prayer of one who forgets the first tashahhud is valid,
and that he should do the prostration of forgetfulness before saying the
tasleem at the end of the prayer. 

In the
answer to question no. 12527 we have quoted the words of Shaykh ibn
‘Uthaymeen (may Allaah have mercy on him) who said:

Thus it
becomes clear that this should be done before the salaam if you have omitted
one of the obligatory parts of the prayer or if you are not sure how many
rak’ahs you have done, and neither of the two choices seems more likely to
be the case. And it should be done after the salaam if you have added
something extra to the prayer or you are not certain but one of the two
choices seems more likely to be the case. 

See
Majmoo’ Fataawa al-Shaykh, 14/14-16 

Based on this, you did well when you did the prostration of
forgetfulness before the salaam, and your prayer is valid in sha Allah. 

And
Allaah knows best.