How will the souls of the disbelievers be restored after their bodies were burned?

Believing that Allah has power over all things, that nothing is beyond Him
on earth or in heaven, that Allah will resurrect those who are in the
graves, that just as He created them from nothing, He is able to resurrect
them however He wills and whenever He wills, and is able to restore them
regardless of what they look like and regardless of how they died, is
something without which belief in Allah is not complete. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

The Muslims and the followers of other religions are all agreed that Allah
has power over all things, as the Qur’an states in many places. End quote. 

Majmoo‘ al-Fataawa
(8/7) 

He
also said: 

Allah created all things, and He has power over all things. Whoever regards
any action as being beyond His capability and beyond His will has
profaned His names and revelations. End quote. 

End quote from Majmoo ‘ al-Fataawa (11/354) 

Allah, may He be glorified and exalted, says (interpretation of the
meaning):

“And he puts
forth for Us a parable, and forgets his own creation. He says: ‘Who will
give life to these bones when they have rotted away and became dust?’

Say: (O Muhammad (blessings and peace of Allah be upon him))
‘He will give life to them Who created them for the first time! And He is
the All-Knower of every creation!’”

[Yaa-Seen 36:78-79]. 

As-Sa‘di said:

This is a specious argument and wrong thinking, to say that this is
far-fetched just because it is beyond human capability. This man said this
by way of heedlessness, forgetting his own origins. Had he thought of his
own creation, after he was nothing, then he came into existence in a
physical sense, he would not have made this suggestion. 

Allah, may He be exalted, responded to this notion that it is far-fetched
with a concise answer, as He said: “Say:
(O Muhammad (blessings and peace of Allah be upon him)) ‘He will give life
to them Who created them for the first time!”.
If you think and reflect upon this verse, you would realise for certain that
the argument is very clear, for the One Who created him the first time is
able to re-create him a second time. That is easier for the power of Allah,
if you think about it. End quote. 

Tafseer as-Sa‘di
(p. 699-700) 

Al-Bukhaari (3481) and Muslim (2756) narrated from Abu Hurayrah (may Allah
be pleased with him) that the Messenger of Allah (blessings and peace of
Allah be upon him) said: “A man who never did any good deeds told his family
that when he died, they should burn him, then scatter half of him on land
and half of him in the sea, for by Allah, if Allah were to seize him, He
would surely punish him as He had never punished anyone in the world. When
the man died, they did what he had instructed them to do, then Allah
commanded the land to gather what was in it, and He commanded the sea to
gather what was in it, then he said (to the man): ‘Why did you do this?’ He
said: ‘For fear of You, O Lord, and You know best.’ So Allah forgave him.” 

According to a version narrated by al-Bukhaari, he said: “When I die, then
burn me and grind up (my bones), then scatter me in the wind.” 

Shaykh al-Islam said: 

This man had doubts and was ignorant of the power of Allah, may He be
exalted, to restore the son of Adam after he had been burned and his remains
scattered, and to re-create and resurrect the deceased if that is done to
him. These are two great principles: 

The first principle has to do with Allah, may He be exalted, namely belief
that He has power over all things. And the second principle has to do with
the Last Day, namely belief that Allah will restore this deceased person and
requite him for his deeds. End quote. 

Majmoo‘ al-Fataawa
(12/491) 

Once a person knows that Allah, may He be glorified and exalted, has power
over all things and that nothing is beyond Him on earth or in heaven, and
that if He wills a thing He says to it: “Be!” and it is, and that He, may He
be glorified, brought all creatures into existence from nothing, it will not
be difficult for him to believe in the resurrection in whatever way it may
occur, without having to think hard or engage in investigations that will
not be to any avail. There is sufficient evidence for him in that which will
never disappear from him, namely his own self. Allah, may He be exalted,
says (interpretation of the meaning): “And
on the earth are signs for those who have Faith with certainty, And also in
your ownselves. Will you not then see?”
[adh-Dhaariyaat 51:20-21]. 

And Allah, may He be glorified and exalted, said to His slave Zakariyya
(peace be upon him) (interpretation of the meaning):

“(Allah said)
‘O Zakariya (Zachariah)! Verily, We give you the glad tidings of a son, His
name will be Yahya (John). We have given that name to none before (him).’

He said: ‘My Lord! How can I have a son, when my wife is
barren, and I have reached the extreme old age.’

He said: ‘So (it will be). Your Lord says; It is easy for Me.
Certainly I have created you before, when you had been nothing!’”

[Maryam 19:7-9]. 

The creation of this boy from a barren mother and an elderly father is not
more strange than the creation of the father and bringing him into existence
from nothing.

See Tafseer at-Tabari (18/151) 

Allah, may He be exalted, said concerning Maryam (interpretation of the
meaning):

“She said: ‘O my Lord! How shall I have a son when no man has
touched me.’ He said: ‘So (it will be) for Allah creates what He wills. When
He has decreed something, He says to it only: “Be!” and it is’”

[Aal ‘Imraan 3:47]. 

And Allah, may He be exalted, says (interpretation of the meaning):

“Verily, the
likeness of ‘Eesa (Jesus) before Allah is the likeness of Adam. He created
him from dust, then (He) said to him: ‘Be!’ – and he was”

[Aal ‘Imraan 3:59]. 

Moreover, these heavens and this earth that are constantly before man’s very
eyes, and what he sees between them of planets and stars, the number of
which no one knows except Allah, for none of His creation can estimate how
great it is, is greater than the creation of people. Therefore it is more
appropriate that the One Who created the heavens and the earth, despite
their greatness and vastness, should be able to re-create man once more. 

Allah, may He be exalted, says (interpretation of the meaning):

“Verily, the
Hour (Day of Judgement) is surely coming, therein is no doubt, yet most men
believe not”

[Ghaafir 40:59].

“Is not He, Who created the heavens and the earth Able to
create the like of them? Yes, indeed! He is the All-Knowing Supreme Creator.

Verily, His Command, when He intends a thing, is only that He
says to it, ‘Be!’ and it is!”

[Yaa-Seen 36:81-82]

“And He it is Who originates the creation, then will repeat
it (after it has been perished), and this is easier for Him”

[ar-Room 30:27].

That is, it is easier for Him. Mujaahid said: Re-creating is easier for Him
than initiating, and initiating was easy for Him. This was also the view of
‘Ikrimah and others. 

Tafseer Ibn Katheer
(6/311) 

Al-Bukhaari (4974) narrated from Abu Hurayrah (may Allah be pleased with
him) that the Prophet (blessings and peace of Allah be upon him) said:

“Allah said: ‘The son of Adam denied Me and he had no right to do so. And he
reviled Me and he had no right to do so. As for his denying Me, it is his
saying: He will not remake me as He made me at first – and the initial
creation (of him) is no easier for Me than the remaking of him. As for his
reviling Me, it is he saying: Allah has begotten a son, while I am the One,
the Eternal. I beget not nor was I begotten, and there is none like unto
Me.’” 

However, if what the questioner meant by his question was: how can the souls
of the disbelievers be restored after their bodies have been burned in the
Fire, i.e., in the Fire on the Day of Resurrection? 

The answer is that their souls will remain in their bodies, even if they are
burned in the Fire. On the Day of Resurrection, when the soul is restored to
the body, it will never leave it again. The soul of the disbeliever will
remain in his body as it is being punished, and the soul of the believer
will remain in his body as he enjoys the bliss of Paradise. 

Every time the skins of the people of Hell are burned through with the Fire,
Allah will replace them with other skins, so that their punishment may
continue without end. Allah, may He be exalted, says (interpretation of the
meaning):

“Surely!
Those who disbelieved in Our Ayat (proofs, evidences, verses, lessons,
signs, revelations, etc.) We shall burn them in Fire. As often as their
skins are roasted through, We shall change them for other skins that they
may taste the punishment. Truly, Allah is Ever Most Powerful, All-Wise”

[an-Nisa’ 4:56]. 

And Allah knows best.