Vato Falman is one of Colonel Roy Mustang's direct subordinates. His rank in the military is warrant officer (later second lieutenant) and he's the resident walking library in Roy's team. If anyone's looking for a date, a fact or whatever, he's the man to ask.
Falman may seem a very strict and serious person, but he's also easy-going and sweet around the people he can trust (i.e. the Roy-tachi). Also, his loyalty and trust towards the Colonel is absolute, supporting him whenever he's needed.
When not around the office, he lives in a dormitory, just as Sergeant Mayor Fuery. It seems he's also in charge of the office supplies. Of course, when Roy gets assigned to Central, Falman is one of the people he chooses to go with him. Aaah, Roy and his amazing!personnel-choosing skills.