All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If the Imaam forgets to make the first Tashahhud and then remembers it after standing up, then he should not sit down to make the first Tashahhud and he should make two prostrations for forgetfulness at the end of the prayer. It is narrated on the authority of Al-Mugheerah ibn Shu‘bah, may Allah be pleased with him, that the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said, “When one of you stands up at the end of two Rak‘ahs: if he remembers before standing straight up, he should sit down; but if he stands straight up, he must not sit down, but perform the two prostrations for forgetfulness.” [Abu Daawood and Ibn Maajah]
However, if the Imaam sits down to make the first Tashahhud after standing upright and before starting to read the Faatihah, intentionally and being aware of what he does, then scholars held different opinions about the ruling of his prayer. Maaliki, Hanbali and some Hanafi scholars said that his prayer is valid. Shaafi‘i and some Hanafi scholars said that his prayer is invalid. The preponderant opinion, however, is that his prayer is valid.
Consequently, the prayer of the Imaam who sat down for making the first Tashahhud after standing up is sound.
As for accusing this Imaam of lying, there is no doubt that lying is forbidden and that it is one of the most evil morals. If it is established that the Imaam is a liar, then he should be advised not to lie, but the prayer that is performed behind him is valid. It will be preferable if you find a righteous Imaam to lead you in prayer. However, if you do not find other than the current Imaam, then you must not quit the congregational prayer at the mosque due to an act of disobedience that he committed.
Nevertheless, you should not hasten to label a Muslim as a liar especially if such a person is religious, because in principle Muslims are free from sin. You should think good of him, for perhaps he did so out of forgetfulness or delusion.
Finally, you should not exaggerate in dealing with the mistakes of Imaams so as to avoid the harms resulting from doing so. For more benefit, refer to Fatwa 105340.