Is it permissible for someone entering the mosque to place his hand on a latecomer who is making up what he missed, in order to lead him, and if not permissible, how does one signal to the follower that he has become his Imam?

"For the newcomer to place his hand on the latecomer to indicate that he has completed the prayer with him, this falls under the category of signaling to the worshiper, which is permissible and preferable to speaking to him. Evidence for this is the action of the Prophet (peace be upon him) when he signaled to the Muslims to complete their prayer, and the hadith of Umm Salamah about the Prophet's (peace be upon him) signaling with his hand to the maidservant. Ibn Rajab and Ibn Hajar clarified that signaling to the worshiper occupies his mind less than speaking, and the permissibility of the worshiper hearing and understanding speech from others does not invalidate his prayer."