Ruling on prayer if one omits some obligatory parts out of ignorance or forgetfulness

If a person makes a mistake in adhkaar that are obligatory in the
prayer, such as the dhikr when sitting between thetwo prostrations and
in the tashahhud – the first part of it – what is the ruling on his
prayer if he forgot or was unaware (that it is obligatory)? What about
previous prayers in which he made this mistake and does he have t o
repeat them?.
Praise be to Allaah.
Firstly:
The dhikr that comes between the two prostrations is one of the
Sunnahs of the prayer andis not obligatory. This has been discussed
previouslyin the answer to question no. 130981
Based on that, if a person omits it deliberately or out of ignorance,
that does not render his prayerinvalid 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 onhim)
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
anomission of something obligatory, because of thegeneral 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 toprostrate, because it never occurred to him to do
it.
End quote from ash-Sharhal-Mumti' 'ala Zaad al-Mustaqni', 3/333, 334
Secondly:
The first Tashahhud is oneof 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. 34570
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 becausehe 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 doesnot 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
thefirst two rak'ahs and did not sit, and the people got up with him.
When hehad finished the prayer and the people were waiting for him to
say thetasleem, he said takbeer whilst sitting and prostrated twice
before saying the salaam, then he said the salaam.
Ibn Qudaamah (may Allahhave 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 byanalogy we apply the same
principle to all the obligatory parts (of the prayer).

And Allah knows best.