Yes, if you have a residence permit in accordance with Section 24 (1) of the German Residence Act (Aufenthaltsgesetz). The provisional document about your right of residence is also your permit. This document that is issued by the immigration office (Ausländerbehörde) must state “Erwerbstätigkeit erlaubt” (employment permitted). This also includes a permit for in-company training. Please note: the period of validity of the residence permit is shorter than the in-company training. A training contract can nevertheless be concluded and entered in the vocational training register.
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