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Upon converting to Islam, all previous sins are forgiven, Alhamdullilah. Additionally, one does not have to makeup any prayers or fasts missed for the duration that one was non-Muslim. The Sacred Law rulings related to worship only apply to Muslims.
After one converted to Islam, if one subsequently missed any obligatory fasts or obligatory prayers, then one ...
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No it's never ever right to offer your fajr prayer after dawn
Even there's a Hadith which says that your namaz is qaza or unofferable after there are no stars left on the sky and the first sun ray has reached the earth!
So try to offer your prayers immediately after Azan because holy prophet said the best deed a Muslim can do is to offer prayer at it's right ...
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