How can one reconcile the virtue of a prayer being answered during the Friday sermon and the obligation to listen attentively to the preacher?

On Friday, there is an hour of response during which no Muslim servant asks Allah for good except that He grants it to him. Scholars have differed regarding its exact time, holding two opinions:

The first: That it is from the time the Imam sits until the prayer concludes. Their evidence is the hadith (definition) of Abu Burdah ibn Abi Musa al-Ash'ari, narrated by Muslim: "It is between the time the Imam sits until the prayer is concluded."

The second: That it is after the Asr prayer. This is the more preponderant opinion, and its evidence is the hadith of Jabir ibn Abdullah, narrated by Abu Dawud and An-Nasa'i: "So seek it in the last hour after Asr."

Based on the opinion that the hour of response is from the time the Imam sits until the prayer concludes, this does not mean that the congregant should busy himself with supplication instead of listening to the sermon. Rather, he should listen to the sermon, say "Ameen" to the Imam's supplication, and supplicate in his prayer. If he adds to that supplication in the last hour after Asr, that is even more preferable and better.