Catalysis of the reaction: (S)-2-(5-amino-1-(5-phospho-D-ribosyl)imidazole-4-carboxamido)succinate = fumarate + 5-amino-1-(5-phospho-D-ribosyl)imidazole-4-carboxamide.
(S)-2-(5-amino-1-(5-phospho-D-ribosyl)imidazole-4-carboxamido)succinate AMP-lyase (fumarate-forming) activity