Final answer:
Guaman Poma de Ayala's legitimacy to write to King Philip III of Spain comes from his firsthand account as an indigenous historian, not from any direct familial connection or invitation.
Step-by-step explanation:
In The First New Chronicle and Good Government, Felipe Guaman Poma de Ayala, also known as Poma, justifies his right to write to King Philip III of Spain (not Spair) by illustrating the injustices occurring at the hands of the Spaniards in Peru.
Poma was an indigenous person who had been Christianized by the Spanish and took it upon himself to detail the history of the Inka and their treatment under colonial rule. His legitimacy is derived not from any familial connections to royalty nor was it a response to a direct invitation by King Philip III. Instead, Poma's authority rests in his firsthand account of the events and his role as an indigenous historian.