Complex sentence: Fallon accepted and Anthrax began writing & recording their next album "Spreading the Disease" at Pyramid Studios in Ithaca, NY, however Fallon left before finishing the album and he was replaced by Joey Belladonna.
Split into simpler sentences: Fallon accepted and Anthrax began writing & recording their next album "Spreading the Disease" at Pyramid Studios in Ithaca, New York. However, Fallon left before finishing the album, and he was replaced by Joey Belladonna.