All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The Prophet prohibited praying after the Fajr prayer until the sun rises above the horizon. The amount of time between the rising of the sun and it being above the horizon in the morning is approximately 15 minutes, and the time between the Fajr prayer and this time varies from one country to another and from one season to another season.
However, you are allowed to make up missed prayers during this time as well as praying any prayer that is perfomed for a reason.
An-Nawawi said in his book entitled Al-Majmoo': 'Of the prayers that are performed for a reason, the missed prayers, whether obligatory or supererogatory, if we say the most sound opinion, it is allowed to make up for the missed supererogatory prayers during this time -i.e. during the time of dislikeability -it is allowed to make up the obligatory prayers, and the supererogatory prayers which are performed before or after the obligatory prayer, and other prayers, and making up for a supererogatory prayer that one always performs. One can also perform the prayer which he vowed to perform, the funeral prayer, the prostration for the recitation of the Quran, the prostration for being grateful to Allaah [Sujood Ash-Shukr], the eclipse prayer and the prayer after finishing the Tawaaf (circumambulation around the Ka'bah). Also, if one performs ablution during this time, he is allowed to pray the two Rak'ah of ablution."
Shaykh Zakariyyah Al-Ansaari said: "This is, as opposed, to the prayers which should be delayed, like the prayer of assuming the state of Ihraam and the Istikhaarah prayer." This means that it is prohibitively disliked to pray these prayers in this time [time of dislikeability]. The prayer is not performed even according to the view that the prayer is only 'slightly disliked' as opposed to 'prohibitively disliked'. However, this is a Dha'eef [weak] opinion.
As regards the mention of Allaah and the recitation of the Quran, they are meritorious during this time and there is no prohibition for them (during this time); the prohibition is specifically related to the prayer.
Allaah Knows best.