@Blickers,
Well, okay. If such would be done in my state, the state would do it via the
Permanent Representation of the State North Rhine-Westphalia to the European Union . If a party, not in our state's government (we've a coalition government, conservative [CDU] and liberals [FDP]) wanted to tell something to other EU-countries, they would use either our state's representation or ... do it as is discussed here.
I haven't seen that letter, just heard/read part of her speech.
My reference to the Foreign Office was just related to "foreign affairs". Brexit is managed by the UK government by an own Department for Exiting the European Union plus various others.