Praise be to Allaah.
The dhikr that comes between the two prostrations is one of
the Sunnahs of the prayer and is not obligatory. This has been discussed
previously in the answer to question no.
Based on that, if a person omits it deliberately or out of
ignorance, that does not render his prayer invalid and he does not have to
do anything. If he forgot it although he usually does it, it is mustahabb
for him to do the two prostrations of forgetfulness before the salaam.
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have
mercy on him) said: If a person omits one of the mustahabb words or actions
out of forgetfulness and he usually does it, then it is prescribed for him
to prostrate (the prostration of forgetfulness) to make up for this omission
that affected the perfection of the prayer but was not an omission of
something obligatory, because of the general meaning of the words of the
Prophet (blessings and peace of Allah be upon him) in the hadeeth, “For
every mistake there are two prostrations”– narrated by Abu Dawood; it is a
hasan hadeeth. In Saheeh Muslim it says: “If one of you forgets, let
him prostrate twice.” As this is general in meaning, if he omits a Sunnah
that he does not usually do, then it is not Sunnah for him to prostrate,
because it never occurred to him to do it.
End quote from ash-Sharh al-Mumti‘ ‘ala Zaad al-Mustaqni‘,
The first Tashahhud is one of the obligatory parts of the
prayer although it is not one of the pillars or essential parts, as was
explained previously in the answer to question no.
If someone omits this obligatory part deliberately, his
prayer is rendered invalid, as you will see in the answer to question no.
9897. If someone omits it
because he forgot, then he has to do the prostration of forgetfulness before
the salaam. If someone omits it because he is unaware of the ruling on it,
he does not have to do anything, because the one who is unaware is excused.
The evidence for the obligatory parts of the prayer being
waived in the case of forgetfulness, and that the prostration of
forgetfulness is required in this case, is the report narrated by
al-Bukhaari (795) and Muslim (570) from ‘Abdullah ibn Buhaynah (may Allah be
pleased with him), according to which the Prophet (blessings and peace of
Allah be upon him) led them in praying Zuhr, then he stood up after the
first two rak‘ahs and did not sit, and the people got up with him. When he
had finished the prayer and the people were waiting for him to say the
tasleem, he said takbeer whilst sitting and prostrated twice before saying
the salaam, then he said the salaam.
Ibn Qudaamah (may Allah have mercy on him) said, concerning
one who omitted the obligatory part deliberately: His prayer is rendered
invalid. But if he omitted it by mistake, he should do the prostration of
forgetfulness before he says the salaam, because of the report narrated by
‘Abdullah ibn Maalik ibn Buhaynah -- and he quoted the hadeeth. Thus this
idea is proven, and by analogy we apply the same principle to all the
obligatory parts (of the prayer).
End quote from al-Kaafi, 1/273
And Allah knows best.