Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Some scholars maintain that the hour of answering du`a on Friday lasts from after `Asr until the sun sets. Other scholars maintain that it lasts from the time when the imam sits on the pulpit to deliver the khutbah (sermon) on Friday until he finishes the Prayer.
In answer to your question, we cite what Sheikh Abdul-`Aziz ibn Baz, the late Mufti of Saudi Arabia, said,
Abu Hurairah reported that the Messenger of Allah (peace and blessings be upon him) mentioned Friday and said, “On this day there is an hour when no Muslim slave stands and prays and asks Allah for something, but Allah will give it to him,” (Ibn Majah) and he gestured with his hand to indicate that whatever he asks for, is as nothing to Allah.
There are two opinions concerning the hour of response (sa`at al-ijabah) on Friday which are likely to be correct:
The first is that it lasts from after Asr until the sun sets, for those who sit and wait for Maghrib, whether in the mosque or at home, making duaa (supplication) to their Lord, whether they are men or women; whoever does that is more deserving of seeing a response to his or her duaa.
The second is that it lasts from the time when the imam sits on the pulpit to deliver the khutbah (sermon) on Friday until he finishes the Prayer.
These two times are more likely to be the times of response on Friday, because of the sound hadiths which indicate that. The hour of response may also be sought at other times of the day; the bounty of Allah is great.
Among the moments when response may come to a duaa in all Prayers, obligatory and nafl alike, is the moment of sujud (prostration), because the Prophet PBUH) said, “The closest that a person may be to his Lord is when he is prostrating, so say a great deal of duaa in prostration (sujud).” (Muslim)
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Muslim also narrated from Ibn Abbas (may Allah be pleased with both father and son) that the Prophet (PBUH) said, “As for ruku (bowing), proclaim the greatness of your Lord in ruku and strive in duaa, for you will be more deserving of being responded to.”
Allah Almighty knows best.
Source: Excerpted with slight editorial modifications from, www.islamqa.info