I found this useful website by Federal Ministry of Labour and Social Affairs that gives an overview about labour market access/law for refugees in Germany. There is also a summary of the most important deadlines and time limits: ****://***.bmas.de/EN/Our-Topics/Fresh-start-in-germany/Ways-for-refugees-to-gain-access-to-the-labour-market.html
The information gathered under the headline “Work permit for asylum applicants & tolerated persons” basically sums up what you need to know. During the first four years (48 months) both Ausländerbehörde and Bundesagentur für Arbeit have to consent with every job offer that you would like to accept. After four years (starting with the 49th month) you get a work permit that doesn’t require the permission by Arbeitsagentur anymore. But Ausländerbehörde still has to agree.
Does that answer your question?
Best wishes, Lea