Firstly: 

It is proven in the Sunnah, in the description of the prayer of the Prophet (blessings and peace of Allah be upon him) that the forefinger should be raised during the tashahhud in the prayer. This issue has been discussed in detail, with evidence, in the answer to questions no. 7570 and 11527 

The fuqaha’ stated that the one who points with his forefinger during any part of the tashahhud has basically fulfilled the Sunnah and has followed the teaching of the Prophet (blessings and peace of Allah be upon him) in his prayer. Rather the discussion is about choosing the point at which one should raise the forefinger; which point is best? 

Shaykh Ahmad al-Barlasi ‘Umayrah ash-Shaafa‘i (d. 957) said: 

Whatever the worshipper does of the ways that are mentioned, he has fulfilled the Sunnah. Rather the difference of opinion is concerning which option is best.

End quote from Haashiyat ‘Umayrah, 1/188. See also: al-Majmoo‘ by an-Nawawi, 3/434. 

This difference of opinion as to which option is best is the matter of ijtihaad and is subject to further examination, because there is no clear text that has been narrated concerning this topic. 

In the hadeeth of Ibn ‘Umar (may Allah be pleased with him) it says that when the Prophet (blessings and peace of Allah be upon him) sat during the prayer, he would place his right hand on his knee and raise the finger that is next to the thumb, offering supplication with it, and his left hand rested flat on his knee. 

Narrated by at-Tirmidhi (no. 249). He said: The hadeeth of Ibn ‘Umar is a hasan ghareeb hadeeth; we do not know of it from the hadeeth of ‘Ubaydullah ibn ‘Umar except via this isnaad. It is to be followed according to some of the scholars among the Companions of the Prophet (blessings and peace of Allah be upon him) and the Taabi‘een, who favoured the view that one should point during the tashahhud. This is also the view of our companions. End quote. 

It was also classed as saheeh by Shaykh al-Albaani in Saheeh at-Tirmidhi. 

The words “and raise the finger that is next to the thumb, offering supplication with it” indicate that raising of the finger begins when reciting the supplication (du‘aa’) in the tashahhud, and the supplication begins with the twin declaration of faith (ash-shahaadatayn), because of what it contains of acknowledgement and affirmation of the Oneness of Allah, may He be glorified and exalted, and that is more likely to be accepted. Then after that, he begins to recite the supplication referred to: “Allaahumma salli ‘ala Muhammad … (O Allah, send blessings upon Muhammad…” until the end of the tashahhud, and until he has completed the tasleem. With regard to the beginning of the tashahhud (“at-tahiyyaatu Lillahi… (all compliments… are due to Allah”)) until we say “… wa ‘ala ‘ibaad illaahi’s-saaliheen (and upon the righteous slaves of Allah”), this is not part of the supplication; rather these are words of praise to Allah and greetings of salaam to His slaves. 

The reports narrated from the Sahaabah and Taabi‘een concerning this matter indicate that what is meant by pointing with the forefinger is an indication of affirmation of Allah’s Oneness (Tawheed) and sincerity. Pointing with one finger is a practical declaration of faith in Allah, the One, Who has no partner or associate. So it is appropriate that starting to point with it should come when starting to say the words of the shahaadah or declaration of faith (“Ashhadu an laa ilaaha ill-Allah (I bear witness that there is no god but Allah)).” 

Hence Ibn ‘Abbaas (may Allah be pleased with him) said: That is sincerity. 

Ibraaheem an-Nakha‘i (may Allah have mercy on him) said: If a man points with his finger during the prayer, it is good and it is an affirmation of the Oneness of Allah (Tawheed).

Narrated by Ibn Abi Shaybah in at-Tasannuf, 2/368 

This is the view of those fuqaha’ who said that pointing with the forefinger should begin when reciting the declaration of belief in the Oneness of Allah. 

As for when to stop (pointing with the finger), the Sahaabah who described the raising of the forefinger did not say that the Prophet (blessings and peace of Allah) lowered it; therefore it should be kept raised until one has finished the tasleem, especially since the latter part of the tashahhud is all supplication (du‘aa’). 

Abu ‘Abdullah al-Khurashi al-Maaliki (d. 1101 AH – may Allah have mercy on him) said: 

From the beginning of the tashahhud until the end, which is (saying) “Ashhadu an laa ilaaha ill-Allah wa anna Muhammadan ‘abduhu wa rasooluhu (I bear witness that there is no God but Allah and that Muhammad is His slave and Messenger)”, and in accordance with what they said, it should continue until the salaam, even if the tashahhud is lengthy. 

End quote from Sharh Mukhtasar Khaleel, 1/288. 

Ash-Shaafa‘i agreed with them that pointing should only begin with the Shahaadatayn (twin declaration of faith), but they addressed the issue in more precise detail, and that may require proof. They said: Starting to raise the finger should only come when reaching the hamzah in the phrase in the shahaadatayn “ila-Allah (but Allah)”. 

Imam an-Nawawi (may Allah have mercy on him) said: 

According to all opinions and views, it is mustahabb to point with the right forefinger, raising it when reaching the hamzah in the phrase Laa ilaaha ill-Allah.

End quote from al-Majmoo‘ Sharh al-Muhadhdhab, 3/434 

Imam ar-Ramli ash-Shaafa‘i (may Allah have mercy on him) said: 

He should raise it when saying “illa-Allah (but Allah)”; he should  begin to raise his finger at the hamzah, thus following what was narrated by Muslim… which clearly indicates that it should remain raised until he stands up (for a third rak‘ah) or says the salaam. What some later scholars tried to prove about lowering it is contrary to what has been narrated.

End quote from Nihaayat al-Muhtaaj, 1/522 

Some of the scholars said that pointing with the finger should start from the beginning of the tashahhud, because the entire tashahhud is a supplication, and it is proven in the hadeeth that he (the Prophet (blessings and peace of Allah be upon him)) used to offer supplication with it. The words at the beginning of the tashahhud (“At-Tahiyyaatu Lillahi…”) are words of praise before offering supplication, so it is part of the supplication and is not something separate. 

Shaykh al-Islam Ibn Taymiyyah (may Allah have mercy on him) said: It is mustahabb to point with one finger during the tashahhud and supplication (du‘aa’).

Al-Ikhtiyaaraat, 38. 

It says in Fataawa al-Lajnah ad-Daa’imah (7/56): 

Pointing with the finger throughout the tashahhud and moving it when offering supplication (du‘aa’), and clenching the other fingers should continue until the salaam. End quote. 

Whatever the case, the matter is subject to ijtihaad and is something concerning which the scholars differed. The different opinions concerning it may have to do with slight differences in the way the prayer is performed, so there is nothing wrong with differing from this ijtihaad and following what one thinks is more correct on the basis of evidence. 

It also says in Fataawa al-Lajnah ad-Daa’imah (5/368): 

Raising the forefinger in the tashahhud is Sunnah, and the reason behind it is to indicate the Oneness of Allah. Whoever wishes may move it and whoever wishes may not move it. This matter should not lead to division and discord between seekers of knowledge. If a person does not raise it at all, or he raises it but does not move it, this is a minor matter that should not lead to denunciation and resentment. However the Sunnah is to raise it throughout the shahaadatayn, until the worshippers says the salaam, as an affirmation of divine Oneness. With regard to moving it, that should be when reciting the supplication, as is narrated in the saheeh Sunnah. 

End quote from Fataawa al-Lajnah, 5/368 

And Allah knows best.