When a person dies, do they [immediately] go to paradise or the hell-fire after their death, or do they remain in the grave until the Day of Judgement? We ask you for clarification of this matter with some additional facts relating to it?

Shaykh Muḥammad ibn Ṣāliḥ al-ʿUthaymīn:

The body of the dead will remain on earth, in the place that it was buried in, until the Day of Judgement. Allāh ﷻ said,

۞ وَنُفِخَ فِي الصُّورِ فَإِذَا هُم مِّنَ الْأَجْدَاثِ إِلَىٰ رَبِّهِمْ يَنسِلُونَ

And the Trumpet will be blown (i.e. the second blowing) and behold! From the graves they will come out quickly to their Lord.” (Q 36:51)

And He ﷻ said,

۞ وَمِن وَرَائِهِم بَرْزَخٌ إِلَىٰ يَوْمِ يُبْعَثُونَ

And behind them is mediary world (barzakh) until the Day when they will be resurrected.” (Q 23:100)

Therefore the body (of the deceased person) will remain on earth. As for their soul, then it is either in Paradise or Hell.

Allāh ﷻ said,

۞الَّذِينَ تَتَوَفَّاهُمُ الْمَلَائِكَةُ طَيِّبِينَ ۙ يَقُولُونَ سَلَامٌ عَلَيْكُمُ ادْخُلُوا الْجَنَّةَ بِمَا كُنتُمْ تَعْمَلُونَ

Those whose lives the angels take while they are in a pious state (i.e. pure from all evil, and worshipping none but Allāh Alone) saying (to them): peace be on you enter you Paradise, because of (the good) which you used to do (in the world).” (Q 16:32)

So Allāh ﷻ has made clear that this statement (of the Angels) will be at the time of death, meaning that they will enter into paradise on the day of their death, and this only for the soul, not for the body. It has also been reported from the Prophet ﷺ that he said: “If the dead person in the grave is a believer, then a door to Paradise will be opened for them, and its comfort and bliss will come to them. As for the non-Muslim, then their soul is (likewise) taken to the punishment.

Allāh ﷻ said about the people of Firʿawn,

۞ النَّارُ يُعْرَضُونَ عَلَيْهَا غُدُوًّا وَعَشِيًّا ۖ وَيَوْمَ تَقُومُ السَّاعَةُ أَدْخِلُوا آلَ فِرْعَوْنَ أَشَدَّ الْعَذَابِ

The Fire; they are exposed to it, morning and afternoon, and on the Day when the Hour will be established (it will be said to the angels): “Cause Fir’awn’s (Pharaoh) people to enter the severest torment!” (Q 40:46)

And He said,

إِنَّ الَّذِينَ تَوَفَّاهُمُ الْمَلَائِكَةُ ظَالِمِي أَنفُسِهِمْ قَالُوا فِيمَ كُنتُمْ ۖ قَالُوا كُنَّا مُسْتَضْعَفِينَ فِي الْأَرْضِ ۚ
۞قَالُوا أَلَمْ تَكُنْ أَرْضُ اللَّهِ وَاسِعَةً فَتُهَاجِرُوا فِيهَا ۚ فَأُولَـٰئِكَ مَأْوَاهُمْ جَهَنَّمُ ۖ وَسَاءَتْ مَصِيرًا

Verily! As for those whom the angels take (in death) while they are wronging themselves (as they stayed among the disbelievers even though emigration was obligatory for them), they (angels) say, “In what (condition) were you?‟ They reply: “We were weak and oppressed on earth.‟ They (angels) say: “Was not the earth of Allāh spacious enough for you to emigrate therein?‟ Such men will find their abode in Hell – What an evil destination!” (Q 4:97)

And He ﷻ also said,

۞وَلَوْ تَرَىٰ إِذْ يَتَوَفَّى الَّذِينَ كَفَرُوا ۙ الْمَلَائِكَةُ يَضْرِبُونَ وُجُوهَهُمْ وَأَدْبَارَهُمْ وَذُوقُوا عَذَابَ الْحَرِيقِ

And if you could see when the angels take away the souls of those who disbelieve (at death), they smite their faces and their backs, (saying): “Taste the punishment of the blazing Fire.” (Q8:50)

So this is evidence that the deceased person who is a believer will meet their reward in Paradise on the day of their death, and the non-Muslim will meet their punishment on the day of their death. This is in regards to the soul. As for the body, then indeed it will remain on earth until the Day of Judgement, and the soul will become reunited with it, either (being) punished or blessed, as the narrations indicate.