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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
There is no basis for this Du‘aa’, and it is impermissible to attribute it to the Messenger of Allaah, sallallaahu ‘alayhi wa salam. It is narrated on the authority of Al-Mugheerah ibn Shu‘bah that the Messenger of Allaah, sallallaahu ‘alayhi wa salam, said: "Whoever tells anything from me, seeing that it is false, then, he is one of the liars." [Ahmad and Ibn Maajah]
The Hadeeth in question clearly seems to be fabricated. According to the religious scholars, among the signs which indicate that the Hadeeth is fabricated is its inclusion of much reward in return for little work, like the statement that "whoever reads this Du‘aa’ after Fajr, ‘Asr and ‘Ishaa’ will be credited as 300, 100, 1000 times Hajj's reward."
Furthermore, it includes some disapproved matters, like the statement that "whoever recites this Du‘aa’ all his missed prayers will be forgiven." Of course, this encourages the common people to neglect prayer and rely on reciting that Du‘aa’; let alone the fact that it includes supplicating Allaah with words that are impermissible to be attributed to Him, like "O Braahaan! O Sultaan! O Musta‘een! O ‘Ajeeb! O Mar’uf!" This is deviation in the names of Allaah The Almighty, and Allaah threatened to punish those who practice deviation in His Names, Saying (what means): {And to Allaah belong the best names, so invoke Him by them. And leave [the company of] those who practice deviation concerning His names. They will be recompensed for what they have been doing.} [Quran 7:180]
Allaah Knows best.