Is the prayer of the congregant valid if the Imam intentionally does something in his prayer that the Imam considers reprehensible and the congregant considers invalid? And is it obligatory for the Imam to inform the congregant of his lack of intention to lead the prayer if the Imam does not consider it a prerequisite?

Prayer is valid behind someone who differs in ancillary matters, even if he does something that the follower deems nullifying, because the Companions and the Tabi'un prayed behind each other despite their differences in ancillary matters.

The Imam is not required to inform the follower that he did not intend to lead the prayer, and the intention of the Imam to lead the prayer is not a condition for the validity of following him in the schools of thought from which fatwas are issued, such as the Maliki, Shafi'i, and Hanafi schools, and one of the two narrations from Ahmad, contrary to what is well-known among the Hanbalis.

If someone prays alone and another person who intends to follow him prays behind him, the congregational prayer is valid and its virtue is attained, because the objective is following.