Ibn Majah

Benefits and Issues:

➊
The companion who performed the prayer was himself Hazrat Qais radi Allahu anhu.
He narrated the incident without mentioning his own name.
In the narration of Jami' al-Tirmidhi, he has stated that this incident happened to him personally. (Jami' al-Tirmidhi, Kitab al-Salat, Chapter: What has been reported about one who misses the two rak‘ahs before Fajr and performs them after the morning prayer, Hadith: 422)

➋
If an action appears to be wrong outwardly,
it is appropriate to seek clarification before expressing displeasure about it,
so that if the explanation is acceptable, there will be no need for admonition.

➌
The silence of the Messenger of Allah sallallahu alayhi wa sallam is evidence of the correctness of that action.
All such matters that came to the knowledge of the Messenger of Allah sallallahu alayhi wa sallam,
and he did not prohibit them,
are all permissible.
These are called "tacitness of the Sunnah" (taqrir al-Sunnah).

English Commentary:
1:
The meaning is that:
After the obligatory (fard) prayer of Fajr, there is no Sunnah or supererogatory (nafl) prayer,
so it will be assumed that you are going to perform another obligatory (fard) prayer after the Fajr obligatory prayer.

2:
This narration indicates that it is permissible to perform both Sunnah rak‘ahs of Fajr after the Fajr prayer but before sunrise,
and what Imam Tirmidhi has said regarding this narration being mursal (with a missing link) and munqati‘ (disconnected) is not correct,
because through the chain of Yahya ibn Sa‘id, this narration is also transmitted with a connected chain (muttasil),
which has been recorded by Ibn Khuzaymah, and through Ibn Khuzaymah, also by Ibn Hibban,
and furthermore, they have also recorded it through another chain.

The Two Sunnah Units of Fajr Missed
It is established from an authentic hadith that if someone misses the two Sunnah units (rak‘ahs) of Fajr and performs them immediately after the obligatory (fard) prayer, it is permissible.
See: [صحيح ابن خزيمه ج2 ص164 ح1116

صحيح ابن حبان الاحسان: 2462 اور المستدرك للحاكم 274/1۔ 275 ح1017]

This has also been declared authentic by al-Hakim and al-Dhahabi.
And the criticism of this narration by Ibn ‘Abd al-Barr is rejected.

...See the original article...

Fatawa ‘Ilmiyyah (Tawdih al-Ahkam), vol. 2, p. 77

1267. Commentary:
➊ If the Sunnah prayers are missed, it is preferable to perform them later, especially the Sunnahs of Fajr, as the Prophet sallallahu alayhi wa sallam did not abandon them even during travel.
➋ It is permissible to perform the Sunnahs of Fajr after the obligatory (fard) prayer, and the hadith in which it is stated, "There is no prayer after the Fajr prayer," refers to general voluntary prayers (nafl), not to such prayers that are being performed for a specific reason.
➌ If one is certain that these will not be missed while waiting for sunrise, then one may delay them. In this way, the hadith "There is no prayer after the Fajr prayer" will also be acted upon.
➍ The silence of the Messenger of Allah sallallahu alayhi wa sallam upon seeing or hearing an action is considered evidence of its approval. Therefore, it is entirely correct to deduce from this hadith that a person who could not perform the two Sunnahs of Fajr before the Fajr prayer may perform them after the obligatory prayer.

Benefit:
It is established from this hadith that the two rak‘ahs after the Fajr prayer (which were supposed to be performed before) can be performed afterwards. Those rak‘ahs which are to be performed before any obligatory prayer, if for some reason they are not performed beforehand, then they can be performed after the obligatory prayer. For example, if the first four rak‘ahs before the Zuhr prayer are missed, it is permissible to perform them after the obligatory prayer. It is not correct for some people to prohibit performing the Sunnah prayers after Fajr. Whatever Islam permits, we should also permit; otherwise, it is sheer misguidance. A tacitly approved hadith (hadith taqririyyah) is part of the Shari‘ah and is a proof.