I would say that "for" should be accepted. "as" could be accepted, though this is not used so much in this function and can be confusing because of its other meanings. "since" should also be accepted.
"A mulher come, pois tem fome." The woman eats because she is hungry.
HOWEVER you will probably NEVER hear a native speaker say this sentence. Native speakers would say "The woman is eating because she's hungry" in almost every context.