Is it a condition to specify the intention for congregational or individual prayer, and if a worshiper catches the congregation in the last Tashahhud and does not catch any rak'ah with the Imam, should he intend to pray in congregation?

For the ma'mum (follower), the intention of following the Imam is required at any point in the prayer where he joins the Imam, such that he is obligated to follow the Imam. If he joins the Imam in the final tashahhud, he makes the takbirat al-ihram behind him and then sits with him for the tashahhud. The intention is divided into the intention of the Imam and the intention of the ma'mum. The worshipper attains the virtue of congregational prayer by doing this.