This technical note is concerned with the fault prognosis problem for partially observed discrete-event systems modeled by unbounded labeled Petri nets. The goal of this problem is to predict the occurrence of each fault before its occurrence. The condition of prognosability provides the necessary and sufficient condition under which any fault can be predicted with no missed detection and no false alarm. In this technical note, we investigate the verification of prognosability for unbounded labeled Petri nets. First, we show that checking prognosability is decidable for Petri net languages. Our approach is based on a reduction from this verification problem to an existing Petri nets model checking problem. Then, we show that the complexity of this problem is EXPSPACE-complete. Our results extend previous works on the verification of language-based prognosability from regular languages to Petri net languages.