I have all of Tarrega's transcriptions in a book called:
OPERE PER CHITARRA.
Vol. 4 - Trascrizioni;
Quarta Edizione Rivedudta e Ampliata
Edizioni BERBEN. Ancona. Italy
This collection contains 92 pieces allegedly arranged by Tarrega himself.
I also have a recording of this Ave Maria played by Fernando Espi on a CD dedicated to 16 of these transcriptions.
Pages 259-260 and 261 contain EXACTLY the same score you put here.
Though it says nowhere in the book, I suspect that the names (Gangi-Carfagna) might refer to the ones who did the fingering. In the case of the Ave Maria they are not the same as the ones you show.