[_ph_]

Almost. The chancellor proposes the ministers, the president appoints them (never not followed the proposal of the chancellor). But she isn't heading a ministry, but reports to the foreign minister, which probably proposed her. She might or might not have the administrative rank as a minister, but she isn't a member of the cabinet.

[DasIch]

https://www.zeit.de/politik/deutschland/2022-02/klimabeauftr... for example mentions that the cabinet appointed her. Of course she isn't part of the cabinet but that is also not what I claimed.