Making up the Sunnah prayer that is done before Zuhr

Firstly: 

It is mustahabb to make up
the regular Sunnah prayers if one misses them, according to the correct
scholarly view. This is the Shaafa’i view and the well known opinion of the
Hanbalis, in contrast to the Hanafis and Maalikis, because of the hadeeth of
Umm Salamah (may Allaah be pleased with her), according to which the Prophet
(peace and blessings of Allaah be upon him) prayed two rak’ahs after
‘Asr. He was asked about them and he said: “O daughter of Abu Umayyah, you
asked about the two rak’ahs after ‘Asr. That is because some people from
‘Abd al-Qays came to me and distracted me from the two rak’ahs that come
after Zuhr; these are they (i.e., I prayed them just now).” Narrated by
al-Bukhaari (1233) and Muslim (834). 

Imam al-Nawawi (may Allaah
have mercy on him) said: 

The correct view in our
opinion is that it is mustahabb to make up the regular naafil prayers. This
was the view of Muhammad, al-Muzani and Ahmad according to one opinion
narrated from him. Abu Haneefah, Maalik and Abu Yoosuf, according to the
most well known view narrated from him, said that they should not be made
up. Our evidence is these saheeh ahaadeeth. End quote. 

Al-Majmoo’
(4/43). 

Al-Mardaawi al-Hanbali (may
Allaah have mercy on him) said: The words “whoever misses any of these
Sunnahs, it is Sunnah for him to make it up” – this is the well known view
of our companions. 

Al-Majd supported this in
his commentary and it was the view favoured by Shaykh Taqiy al-Deen – i.e.,
Ibn Taymiyah. End quote from al-Insaaf (2/187). 

Shaykh Ibn ‘Uthaymeen (may
Allaah have mercy on him) said: 

Making up regular Sunnah
prayers is Sunnah if one misses them. The evidence for that is that when the
Prophet (peace and blessings of Allaah be upon him) slept and missed
Fajr prayer, and did not wake up until after the sun had risen, he prayed
the Sunnah prayer of Fajr first, then he prayed Fajr after that. End quote. 

Liqaa’aat al-Baab
il-Maftooh (no. 74, question no 18). See also
al-Mawsoo’ah al-Fiqhiyyah (25/284). 

Secondly: 

If he wants to make up the
Sunnah prayer that comes before Zuhr after offering the fard Zuhr prayer,
should he pray the Sunnah prayer that comes before Zuhr first, and then the
Sunnah prayer that comes after Zuhr, or vice versa? 

It seems that this matter
is broad in scope, whether he starts with the Sunnah prayer that comes
before or that which comes after, because what matters is doing it, whether
it is done sooner or later. 

Shaykh Ibn ‘Uthaymeen (may
Allaah have mercy on him) said: 

The scholars said: If you
miss the two rak’ahs that come before Zuhr, then pray them after the prayer,
because you were excused from doing them before the prayer. This happens all
the time: a person comes to the mosque and finds that they have already
started the prayer. In this case, he should make them up after he prays
Zuhr. 

But he should offer the
regular Sunnah prayer that comes after Zuhr before the regular Sunnah prayer
that comes before. 

A man comes and the people
are praying, and he is not able to offer the Sunnah prayer of Zuhr. When he
has prayed Zuhr, he should pray two rak’ahs with the intention of offering
the regular Sunnah prayer that comes after Zuhr, then make up the regular
sunnah prayer that comes before. This was narrated from the Prophet
(peace and blessings of Allaah be upon him) in a hadeeth narrated by Ibn
Majaah. 

Fath Dhi’l-Jalaal
wa’l-Ikraam bi Sharhh Buloogh al-Maraam (2/225). 

And Allaah knows best.