He wants to continue fasting so that he can give up smoking

If what is
meant is fasting every day, so that you continue fasting continuously without
breaking the fast except on days when fasting is forbidden, such as the two
Eids and the days of at-tashreeq (the three days following Eid al-Adha), then
the more correct scholarly view is that it is makrooh and is not allowed.

For more
information please see the answer to question no. 144592

But if what
you meant is continuing to fast for part of the year, there is nothing wrong
with that, as it is confirmed by the Sunnah. Al-Bukhaari (1806) and Muslim
(1890) narrated from ‘Aa’ishah (may Allah be pleased with her) that Hamzah ibn
‘Amr al-Aslami asked the Messenger of Allah (blessings and peace of Allah be
upon him): O Messenger of Allah, I am a man who fasts continually for periods
of time; can I fast when travelling? He said: “Fast if you wish and do not fast
if you wish.”

An-Nasaa’i
(2319) narrated from Usaamah ibn Zayd that the Messenger of Allah (blessings
and peace of Allah be upon him) used to fast continuously until it was said
that he would not break the fast, and then he refrain from fasting until it was
said that he would not fast.

Classed as
saheeh by al-Albaani in Saheeh an-Nasaa’i.

Al-Bukhaari
(1833) and Muslim (1956) narrated that ‘Aa’ishah (may Allah be pleased with
her) said: The Messenger of Allah (blessings and peace of Allah be upon him)
used to fast until we said that he would not break the fast, and he used to
refrain from fasting until we said that he would not fast. And I never saw the
Messenger of Allah (blessings and peace of Allah be upon him) fast any month in
full except Ramadan, and I never saw him fast more than he did in Sha‘baan.

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

With regard to
fasting continuously for part of the year, this is something that the Prophet
(blessings and peace of Allah be upon him) used to do. He would fast until one
would think that he would not break the fast, and he would refrain from fasting
until one would think that he would not fast. Similarly, he would spend some
entire nights in prayer (qiyaam), such as the last ten nights of Ramadan, and
he would spend other nights in prayer occasionally. This is what is mentioned
in as-Sunan.

End quote from
Majmoo‘ al-Fataawa, 22/304

Better than
that is the fast of the Prophet of Allah Dawood (peace be upon him). He used to
fast one day and not the next. Al-Bukhaari (1841) and Muslim (1962) narrated
from ‘Abdullah ibn ‘Amr (may Allah be pleased with him): News reached the
Prophet (blessings and peace of Allah be upon him) that I was fasting
continually and spending every night in prayer. Either he sent for me or I met
him and he said: “Have I not been informed that you fast and do not break the
fast, and that you pray? Fast (some days) and do not fast (some other days),
pray (qiyaam) for part of the night and sleep. For your eyes have a right over you
and your soul has a right over you and your family has a right over you.” He
said: I have the strength to do that. He said: “Then observe the fast of
Dawood, peace be upon him. He said: How (did he fast)? He said: “He used to
fast one day and not fast one day, and he did not flee if he met (the enemy in
battle).”

According to
another report, “It is the proper way of fasting.” Narrated by al-Bukhaari
(3165) and Muslim (1962)

According to
another report, “There is nothing better than that.” Narrated by al-Bukhaari
(1840) and Muslim (1962)

Ibn al-Qayyim
(may Allah have mercy on him) said:

It is proven
in as-Saheehayn that the Prophet (blessings and peace of Allah be upon
him) said: “The best kind of fast is the fast of Dawood.” According to another
version: “There is nothing better than the fast of Dawood; he used to fast one
day and not the next.” This clear saheeh text that dispels all doubt shows that
fasting one day and not the next (i.e., fasting alternate days) is better than
fasting continually.

End quote from
Tahdheeb as-Sunan, 7/71

But the best
advice for each individual is that he should choose for himself the naafil acts
of worship that he is able to do and persist in, and he should not take upon
himself that which will prevent him from doing other kinds of good deeds.

So look at
what you are able to do and strive to do it; seek to do naafil acts of worship
that are proven in reports from the Prophet (blessings and peace of Allah be
upon him), with regard to fasting and other deeds.

With regard to
giving up smoking, that is a good thing and we encourage you to go ahead with
it; be determined and be firm with yourself concerning it. There is no doubt
that fasting will help you to a great extent with that. Try to keep yourself
busy with acts of worship and find a good environment so that you will not be
tempted to go back to this bad habit.

See also the
answer to question no. 47565

And Allah knows best.