Can I touch a person to pray in congregation with him if I missed the first congregational prayer?
A person who is late for prayer and has not joined the Imam (leader of Prayer) in the first rak`ah (unit of prayer) is known as masbuq. If a person joined the imam in the second, third, or fourth rak`ah, he stands up after the tasleem (end of prayer) and offers the rak`ahs he missed.
Abu Hurairah (may Allah be pleased with him) narrated: I heard the Messenger of Allah (peace be upon him) saying, “When the Iqamah is pronounced, do not come to it running, you should walk calmly with tranquility to join the congregation. Then join in what you catch for and complete what you miss.” (Agreed Upon)
Responding to this Question, Dr. Muhammad Salah says that it is permissible for a latecomer who does not catch the prayer to gently touch a person in front of him to offer congregational prayer.
Source: Iqra Youtube Channel.