The correct designation is Fliegerverbindungsoffizier.
Fliegerverbindungsoffiziere and Fliegerleitoffiziere had different responsibilities.
A Fliegerleitoffizier was solely a Forward Air Controller.
According to the link posted above a Fliegerverbindungsoffizier (Flivo) attached to a division could be used in this role too, but he was also a liason officer between Armee and Luftwaffe.
As far as I know Flivos existed on different levels, both in divisions and in armies.
The following information refers to a Flivo attached to an Army:
Found here:
http://www.wiki.luftwaffedata.co.uk/wiki/index.php?title=Flivo
"This position was created as part of the re-organisation that took place in Apr/May 1942.
Luftwaffe Staff officer (usually an Oberst) attached to an Armee Gruppe, Armee or Panzerarmee - responsible for the following:-
1. Liaison between the Armee Gruppe and the Fliegerkorps or Luftflotte operating within the area of the Armees control.
2. Briefing the Armee headquarters on the local air situation, the operational intentions of the Fliegerkorps or Luftflotte and its order of battle.
3. Passing to the Fliegerkorps or Luftflotte the Armee Gruppes wishes with regard to luftwaffe operations and any air transport requirements.
4. Briefing the Fliegerkorps or Luftflotte with regard to the ground situation within the Armeegruppes area of control, its operational intentions and the order of battle of the Armee formations.
5. Employment of the aircraft of the Kurrierstaffel attached to the headquarters of the Armee Gruppe.
6. Co-operation and co-ordinatioon with the Armees Quartermaster branch. "
I will see if I can also find information on the responsibilities of a Flivo in an army division.