Is it essential with regard to the Sunnah prayers that are done before the fard prayer that the time for that fard prayer should have begun?

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Check below answers in case you are looking for other related questions:
The time of Duha prayer
How to offer the daytime four-rak’ah prayers

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Should he do more tawaaf or more prayers in al-Masjid al-Haraam?
He started to observe a naafil (supererogatory) fast then he was invited to eat and he ate
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The time of Duha prayer
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