Praise be to Allah.
The proven Sunnah, as narrated in mutawatir reports from our Prophet (blessings and peace of Allah be upon him) is that he used to say takbir when starting to pray, and for the movements in the prayer. He would say “Allahu akbar.” Adding anything to that, such as saying “Allahu akbaru kabira” or “Allahu akbar al-‘Azim” or “…al-Mu‘ti” is an innovation and is to be rejected, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever introduces anything into this matter of ours that is not part of it, it will be rejected.” (Narrated by al-Bukhari (2697) and Muslim (1718)
And the Prophet (blessings and peace of Allah be upon him) said: “Whoever does anything that is not in accordance with this matter of ours, it will be rejected.” (Narrated by Muslim, 1718)
And he said: “Whoever among you lives after I am gone will see great differences; you must adhere to my Sunnah and the way of the Rightly Guided Caliphs. Hold on to it and cling fast to it. And beware of newly-invented matters, for every newly-invented matter is an innovation and every innovation is a going astray.” (Narrated by Abu Dawud, (4607), at-Tirmidhi (2676) and Ibn Majah (42)
Innovation (bid‘ah) is haram, and the one who introduces an innovation is sinning, but his prayer is still valid if he does that, as was stated by the scholars.
An-Nawawi (may Allah have mercy on him) said in al-Majmu‘ (3/292):
“If he says takbir and adds something that does not change it, so he says, “Allahu akbar wa ajall wa a‘zam (Allah is most great, most majestic and most mighty),” or “Allahu akbaru kabira (Allah is most great indeed),” or “Allahu akbaru min kulli shay’ (Allah is greater than all things),” it will be acceptable, and there is no difference of scholarly opinion concerning that, because he has said the takbir and has added something that does not change it.”
Al-Bahuti (may Allah have mercy on him) said in Kashshaf al-Qina‘ (1/330):
“If he adds something to the takbir, such as saying “Allahu akbaru kabira” or “Allahu akbar wa a‘zam (Allah is most great and most mighty)” or “… ajall (most majestic)” and the like, it is makruh (disliked) for him to do that, because it is an innovation.”
To sum up, it is not permissible to add anything to the takbir. The one who does that has introduced something new and has innovated something (bid‘ah ), but his prayer is still valid.
And Allah knows best.