Ruling on offering supplication between the two prostrations
Question

I read on your website that you say that it is fard (obligatory) for the worshipper to say “Rabb ighfir li, Rabb ighfir li (Lord forgive me, Lord forgive me), but the teacher in our mosque says that this is Sunnah and it is not fard. What is your evidence?
Praise be to Allah.Offering supplication between the two prostrations is one of the proven Sunnahs of the Prophet (blessings and peace of Allah be upon him), and has been soundly narrated from him in a number of hadiths.
These hadiths include the report narrated from Ibn ‘Abbaas (may Allah be pleased with him), according to which the Prophet (blessings and peace of Allah be upon him) used to say between the two prostrations: “Allaahumm ighfir li warhamni wajburni wahdini warzuqni (O Allah, forgive me, have mercy on me, console me, guide me, and grant me provision).” Narrated by at-Tirmidhi (284); classed as hasan by al-Albaani.
Several versions of this hadith have been narrated, some of which include more phrases than others. In total, what has been narrated regarding this supplication is seven phrases: “Allaahumm ighfir li warhamni wajburni wahdini warzuqni wa ‘aafini warfa‘ni (O Allah, forgive me, have mercy on me, console me, guide me, grant me provision, grant me wellbeing and raise me in status).”
See: Sunan at-Tirmidhi (284), Abu Dawood (850) and Ibn Maajah (888).
An-Nawawi said: To be on the safe side, meaning to make sure that one is doing it in accordance with the Sunnah, you should try to recite all the phrases that are mentioned in all versions of the hadith, which is seven phrases." (Al-Majmoo‘  3/437).
Shaykh al-Albaani (may Allah have mercy on him) said something similar in Sifat as-Salaah, p. 153.
The minimum that may be said is “Rabb ighfir li (Lord forgive me),” because of the report narrated from Hudhayfah, according to which the Prophet (blessings and peace of Allah be upon him) used to say between the two prostrations: “Rabb ighfir li, Rabb ighfir li (Lord forgive me, Lord forgive me).” Narrated by an-Nasaa’i (1145), classed as saheeh by al-Albaani in Sifat as-Salaah (3/118).
The scholars differed concerning the ruling on this supplication.
The majority of scholars are of the view that this supplication is recommended (mustahabb), and is not one of the obligatory parts of the prayer.
The Hanbalis are of the view that it is obligatory because the Prophet (blessings and peace of Allah be upon him) always offered supplication between the two prostrations, and because in all the actions of the prayer there is always some remembrance of Allah (dhikr), and all these words of dhikr are obligatory, so the ruling on the dhikr between the two supplications comes under the same ruling.
So what is obligatory is to say “Rabb ighfir li (Lord forgive me)” once, and anything in addition to that is recommended.
The view of the majority, which is that it is recommended, is a view that has strength, because there is no clear evidence to indicate that it is obligatory. This is the view favoured by some of the Hanbalis too.
Al-Haafiz Ibn Rajab said: The ruling on this dhikr between the two prostrations, according to most of the companions of Ahmad, is the same as the ruling on the tasbeeh when bowing and prostrating, which is that it is obligatory; the prayer is rendered invalid if it is omitted deliberately, and the prostration of forgetfulness must be done if it is omitted by mistake. It was also narrated from Ahmad that it is not obligatory.
Harb said: The view of Ahmad is that if [the worshipper] says it, it is permissible, and if he does not say it, it is permissible. In his view, the matter is flexible.
Similarly, Abu Bakr al-Khallaal stated that this is the view of Ahmad, and it is also the view of the majority of scholars."(Fath al-Baari by Ibn Rajab  6/56).
Such issues should not become a matter of dispute and dissent among the Muslims, because each view has evidence that carries weight according to sharia, and if someone is convinced of one of the two views, there is no blame on him for acting in accordance with it.
As for what you mention about there being an answer on our website stating that it is obligatory, that is not correct. What it says is that this dhikr is waajib and not fard, as noted in the answer to question no. 65847 .
The difference between them is that what is fard cannot be waived deliberately or by mistake; rather it must be done.
What is waajib is waived if one forgets, and it may be made up for by doing the prostration of forgetfulness. And Allah knows best.
We noted that there, and we also noted that this is an issue concerning which there is a considerable difference of opinion among the scholars:
There are some differences of opinion among the fuqaha’ regarding some of these issues; what is regarded as obligatory (waajib) by some is regarded as Sunnah by others. This is discussed in detail in the books of fiqh.
And Allah knows best.