They are the labour department. Like I said, things have changed since I worked with work permits. I understand from a colleague that she went to the MIgartionsamt for info, In the old days, we (i.e.the employers) applied for permits through the Arbeitsamt. The cycle was so.
Arbeitsamt - BFA - Arbeitsamt - cannot remember if it came back to us straight after that or if had to be cleared by the cantonal authorities first. The process took 4 -6 weeks. Like i said before, things have changed since.