Is there a female yeast infection that can be passed to a male and then back and forth. Specifically, can the male spread the yeast infection to another female. Can a yeast infection act the same as a sexually transmitted disease?

Yes, happens every day, and the male often shows no symptoms.
He needs to treat himself the same way the woman does - he can talk to a pharmacist if he won't get tested.

Absolutely! Get both the male and the female treated.