I am not an authority on Islam, but found this in an authentic site.
If one assumes that he may miss the second rakaat or tashahhud of the
second rakaat of the Fajr fardh salaah and he has not completed the
sajdah of the second rakaat of the sunnah salaah, he should break his
sunnah salaah and join the jamaat (congregation) of the Fajr fardh
salaah.However, it will be waajib (imperative) to repeat the sunnah
salaah that was abandoned to join the fardh salaah.
It is advisable to perform the sunnah salaah while the jamaat has
already commenced outside the demarcated masjid area as it is makrooh
(abominable) to pray the two rakaat of sunnah in the demarcated masjid
area. You may perform the Sunnah salaah in the sehn (courtyard area)
or some other place of the masjid.
If the Fajr fardh salaah was missed together with the sunnah salaah,
then both the sunnah and the Fajr qadha should be performed after
sunrise until the pre-zawaal time .After the zawaal time, the
performance of only the fardh salaah remains obligatory and not the
If only the fardh salaah was missed and not the sunnah salaah, then
the qadha of the fardh salaah can be performed at any time provided it
is not in the non-permissible times(makrooh) which are :
zawaal(zenithal time), sunrise and sunset.
It will be makrooh tanzeehi(undesirable) to perform the two rakaats
sunnah of the fajr salaah after the performance of the fajr fardh
salaah until sunrise. One should perform the missed sunnah salaah
after sunrise until the pre-zawaal time.
In future, prepare well in advance for the Fajr fardh salaah in order
to avoid such circumstances. Rasullullah (s.a.w) has greatly
emphasized the performance of the two rakaat sunnah of the Fajr
You can get the original Q&A and related references here, http://www.askimam.org/public/question_detail/19539