Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Salaat al-Ishraq is a name used by some scholars for the Prayer after the sun has risen (approximately 20 minutes after sunrise); others refer to it as salaat ad-duha.
Anas ibn Malik narrated that the Prophet (peace and blessings be upon him) said, “Whoever prays the dawn prayer in congregation and then continues to make dhikr until sun has fully risen and then prays two rak`ahs, he will gain rewards of a full Hajj and `Umrah combined.” (At-Tirmidhi)
Although some Hadith critics question the authenticity of this hadith, some scholars consider it as sound since it has been strengthened by other reports.
There is no need to reject it, since this is the same prayer that is called salat ad-duha, which has been supported by authentic traditions that have been widely accepted by scholars.
The last group of scholars, however, does not make any distinction between ishraq and duha prayers. They are of the view that the time of duha begins after sun has risen fully (as mentioned above) and ends close to zawal (when the sun reaches the meridian).
So, never mind the terminology, it is recommended to pray a few rak’ahs after sunrise.
Allah Almighty knows best.