What is legally preferable for one who is late for Friday prayer until after the Imam ascends the pulpit, due to a reason other than travel: praying four rak'ahs outside the mosque, or joining the mosque and catching up with whatever remains of the two sermons and the prayer?

The Friday prayer is not missed by the Imam ascending the pulpit or by the end of the two sermons. Whoever catches one rak'ah with the Imam has caught the Friday prayer. Whoever is obligated to attend the Friday prayer must strive to do so, even if they only catch one rak'ah. They are sinful if they fail to attend without a valid excuse and pray Dhuhr as four rak'ahs instead. The reward for hastening to the Friday prayer is great, as the Prophet, peace and blessings be upon him, said: "Whoever bathes on Friday with the bathing of Janabah, then goes early, it is as if he sacrificed a camel..." [the rest of the Hadith]. Moreover, failing to attend it seals the hearts and makes those who stay behind among the negligent.