Can My Mother Become Catholic?

Based on the information provided it would appear that your mother is civilly married to a divorced man.

Your mother has received a decree of nullity so she is free to marry in the Church. If her husband was previously married and divorced then he would need to obtain a decree of nullity (annulment) for his prior marriage(s). This, of course, assumes that the previous spouse is still living.

He is not required to become a Catholic in order for your mother to convert or marry him in the Church. However, marriage is a sacrament that is binding on any person who enters into it. He is still presumed to be married to his first wife until an annulment case is able to prove otherwise. Your mother would need to straighten out her marital situation prior to being accepted into the Church.