Is the brother's prayer valid if he was led by someone who intended to pray but did not actually pray, rather he only pretended to pray, even though the Imam who pretended was the one who established the prayer and audibly recited the transition takbeers?

It is permissible for you to conceal your past missed prayers, and you may use circumlocution (ta'rid). It would have been better for you to pray with him, intending for it to be a supererogatory prayer for you. Your brother's prayer is valid. If a follower experiences a ritual impurity or his prayer becomes invalid, he is permitted to break off and complete his prayer individually. The Imam's prayer is not invalidated by the invalidation of the follower's prayer, and the Imam's intention to lead is not a condition for the validity of following him. An error in the intention of leading does not harm. The majority of scholars hold that congregational prayer is not obligatory to be performed in the mosque; rather, it suffices to perform it anywhere, although witnessing the prayer in mosques is superior.