According to the available evidence, Allaah The Almighty did not send a prophet to humans and Jinn except Prophet Muhammad, sallallaahu ‘alayhi wa sallam, who said that "every prophet was sent to his nation, except for him;  he was sent to all mankind". [Al-Bukhari & Muslim]

Another narration of the Hadeeth mentions that the Prophet sallallaahu ‘alayhi wa sallam,  was sent to: "The Red and the Black"  Mujaahid said that the meaning of this is that he was sent to the Jinn and humans, another interpretation of the Hadeeth suggests that the "Red and the black" refers to  Arabs and non-Arabs.

Allaah The Almighty sent the Prophet, sallallaahu ‘alayhi wa sallam, to humans, Jinns; Arabs and non-Arabs— unlike other prophets. Ibn ‘Abdul-Barr said that there is no disagreement among scholars as to whether or not the Prophet, sallallaahu ‘alayhi wa sallam, was sent to humans and Jinns. 

The fact that every prophet was sent to his nation does not mean that no one outside a prophet's nation believed in him, or that a prophet was not allowed to call a person outside his nation to believe in Allaah The Almighty.

Consequently, what was mentioned above does not contradict the fact that Jinns believed in Moosa (Moses) although Moosa was not sent to the Jinn. Moosa was sent to the children of Israa’eel (Israel). Allaah The Almighty Says (what means): {They said, "O our people, indeed we have heard a [recited] Book revealed after Moses.} [Quran 46:30]

‘Ataa’ said that some Jinn had been Jewish and then became Muslims. Commenting on this verse, {We were [of] divided ways.} [Quran 72:11], Ibn Al-Musayyib said that it meant that the Jinn were Muslims, Jewish, Christians and Magians.

Allaah Knows best.