Is it incumbent upon a Muslim to remain in the mosque after the Friday prayer concludes until the Imam leaves the mihrab in order to receive the full reward of Jumu'ah, and is there any basis for this act in Islamic law?

The reward of Friday prayer is missed and diminished by fidgeting, talking, not listening during the sermon, and being late for it. In the Hadith: "If you say to your companion: 'Be silent on Friday,' while the Imam is delivering the sermon, you have engaged in idle talk. And whoever touches pebbles has engaged in idle talk." And in a narration: "Whoever engages in idle talk has no Friday [reward]"; meaning, not a complete reward. This is supported by what Ibn Hibban narrated from Jabir (may Allah be pleased with him), that Abdullah ibn Mas'ud (may Allah be pleased with him) entered the mosque while the Prophet (peace be upon him) was delivering the sermon. He asked Ubayy ibn Ka'b about something, but Ubayy did not respond to him. After the prayer, Ubayy said to him: "You have not attended the Friday prayer [properly]." When Ibn Mas'ud asked the Prophet (peace be upon him), he said: "Ubayy spoke the truth, Ubayy spoke the truth, obey Ubayy." And in another narration: "You will get nothing from your Friday [prayer] except what you engaged in idle talk." And Ibn Abd al-Barr says: "This is understood to mean that he does not receive the reward of one who prayed Friday and listened attentively, not that his prayer is invalidated."

As for the departure of the congregant before the Imam leaves the mihrab, there is no evidence that the reward is lost or diminished by that. Rather, it is recommended for the congregant not to leave before the Imam, unless the Imam prolongs his sitting. This is evidenced by his (peace be upon him) saying: "I am your Imam, so do not precede me in bowing, nor in prostrating, nor in standing, nor in departing."