Praise be to Allah.
Standing in the obligatory prayer is a pillar or essential part thereof without which the prayer is not valid. So it is not permissible for anyone to pray sitting unless he is not able to stand.
See the answer to question no. 67934.
The scholars have stated that it is obligatory to stand for the opening takbeer in the obligatory prayer.
An-Nawawi (may Allah have mercy on him) said in al-Majmoo‘ (3/296): It is obligatory to say the opening takbeer correctly, pronouncing all the letters, whilst standing. If the worshipper pronounces any letter of it when he is not standing, then he has not started to pray. End quote.
Al-Akhdari al-Maaliki said: The obligatory parts of the prayer are: the intention (niyyah) to offer a specific prayer; saying the opening takbeer (takbeerat al-ihraam) whilst standing; reciting al-Faatihah whilst standing; bowing… End quote.
Al-Kharashi (may Allah have mercy on him) said in Sharh Mukhtasar Khaleel (1/264), discussing the obligatory parts of the prayer:
Standing for the opening takbeer in the obligatory prayer, for one who is able to stand and is not joining the congregational prayer late, is obligatory. Therefore it is not acceptable to say it whilst sitting or leaning forward. End quote.
In al-Mawsoo‘ah al-Fiqhiyyah al-Kuwaitiyyah (13/220) it says: It is obligatory for the worshipper to say takbeer whilst standing, in prayers in which it is obligatory for him to stand, because the Prophet (blessings and peace of Allah be upon him) said to ‘Imraan ibn Husayn, who was suffering from haemorrhoids: “Pray standing and if you cannot, then sitting, and if you cannot, then lying on your side.” An-Nasaa’i added: “… and if you cannot, then lying on your back.” Standing is done by making the back straight.
So it is not permissible to say the opening takbeer whilst sitting or bending forward, and when standing is mentioned, it includes that which may take its place, such as sitting in obligatory prayers when one has an excuse. End quote.
The basic principle with regard to the prayer of one who is sick is that he must do what he is able to of the obligatory and essential parts of the prayer, and whatever he is unable to do is waived in his case.
So if he is able to start the prayer standing, he must do that, then if it becomes difficult for him to remain standing, he may sit down.
See the answer to question no. 263252.
It says in Mukhtasar Khaleel (a Maaliki book): If he is unable to recite al-Faatihah whilst standing, he may sit.
Al-Hattaab said in his commentary:
Ibn ‘Abd as-Salaam said: What he should do in that case is:
If he is able to stand for any length of time, he must do that, whether he is able to say the opening takbeer [whilst standing] only, or he is able to do more than that, because what is required is only to stand whilst reciting, so if he is unable to stand for the entire time whilst reciting, he should stand as long as he is able to, and the rest is waived in his case. End quote.
Ibn Farhoon said: That is, if he is unable to complete at-Faatihah standing, but he is able to recite it sitting, because he becomes dizzy and the like, then the well-known view is that he should recite as much of it as he is able to [whilst standing], and standing is waived in his case for the rest of it, and he may recite [the rest of it] whilst sitting.
Note: the apparent meaning of the author’s words is that standing is waived for him throughout, even when saying the opening takbeer, but that is not the case, unless his words are referring to a case where if a person stands [to say the opening takbeer], he will not be able to sit down after that.
End quote from Mawaahib al-Jaleel (2/5).
In al-Fataawa al-Hindiyyah (1/136) – which is a Hanafi book – it says:
Chapter 14: Prayer of a sick person.
If the sick person is unable to stand, he may pray seated, bowing and prostrating [from a seated posture], as it says in al-Hidaayah.
The soundest of these scholarly views concerning the meaning of incapability is that what is meant is if he will suffer harm as a result of standing.
But if it is somewhat difficult for him to stand, it is not permissible for him to refrain from standing, as it says in al-Kaafi.
If he is able to stand for part of the time, but not to complete it, then he should be told to stand as long as he is able to, even if he is only able to say the takbeer whilst standing, and is not able to stand for the recitation, or if he is able to stand for part of the recitation but not for the entire duration thereof. In that case he should be told to say the takbeer whilst standing, and to recite as much as he is able to whilst standing, then to sit down when he becomes unable to remain standing. End quote.
Shaykh Muhammad Mukhtaar ash-Shinqeeti said:
The one who has an excuse and is not able to stand may pray seated.
If he is able to stand for the opening takbeer, then he should not come [into the mosque] and sit down straightaway and say the opening takbeer; rather he should say the takbeer whilst standing, because he is able to do so whilst standing, then he should sit down when it becomes too difficult for him to remain standing. If it is not possible or it is too difficult for him to stand, as in the case of one who is paralyzed, then he may say the takbeer whilst seated. But if he is able to stand, then he should stand with the chair behind him, and there is nothing wrong with that, then when it becomes too difficult to remain standing, he may sit back down, in accordance with the basic principle of fiqh, “Concessions should be commensurate with the degree of necessity”, from which is derived the principle that when something becomes permissible because of need, it only becomes permissible to the degree to which it is necessary.
If the necessity in this case is that standing is too difficult for him, we say: Say takbeer whilst standing, then sit down.
But if necessity in this case means that he is unable to stand at all, then we say: Say takbeer whilst seated, and there is no blame on you.
In the first scenario, in the concession is commensurate with the necessity, and in the second scenario, the concession is commensurate with the necessity. That should be made clear to people, because you may see someone saying takbeer whilst seated even though he is able to stand, or you may seen him get up after the prayer, pick up the chair and carry it out. In that case, there is no concession allowing him to do the essential part of the prayer, which is the opening takbeer, whilst seated. This should be pointed out to him, and if he is unable to stand, we say that he may pray seated.
End quote from Sharh Zaad al-Mustaqni‘ (2/91).
Based on the above, your father has to repeat this prayer in which he forgot to stand for the opening takbeer, if he was aware that it was obligatory for him to stand for the opening takbeer.
But if he prayed sitting down because he was unaware of the shar‘i ruling, and he thought that because it was permissible for him to sit down that he could say the opening takbeer whilst sitting, then he does not have to repeat the prayer.
See also the answers to questions no. 45648, 193008 and 50684.
And Allah knows best.