The rule is that citizens of non-EU countries are not allowed simply to enter the Federal Republic of Germany and work there. They must apply for a work visa before they enter the country. This also applies for holders of a travel document for refugees issued by another EU state, for example Greece.
Is it true that people who are recognised as refugees in Greece are allowed to work in Germany?
No. The rule is that citizens of non-EU countries are not allowed simply to enter the Federal Republic of Germany and work there. They must apply for a work visa before they enter the country. This also applies for holders of a travel document for refugees issued by another EU state, for example Greece.
Further information about work visas is available here:
https://www.auswaertiges-amt.de/en/aamt/zugastimaa/buergerservice/faq/-/606852