Can my friend get work permit from federal employment agency

My friend from Gambia got his application rejected by BA and his 6 months job seeker visa expired and he is on Fiktionbescheinigung after the expired visa, he got another job and send to BA. The first letter of rejection stated that he have to return to his country and stay for six months.

Can they approve his job offer since he still have a valid fiktionbescheinigung that have not expired although the normal 6 months job seeker visa have expired. He continue looking for job with fiktiobescheinigung and got one.

Only a few visa types can be converted to work permit - the JSV is one of them (family reunion visa is another), but a Fiktionsbescheinigung is not.
Thus he has to leave the EU and apply at a German embassy there, preferably in his own country.