There's nothing grammatically wrong with your English
sentence, but it sounds too much like an over-literal translation from Czech.
The short chain of abstract noun + of („the maintenance of the value
of …“) makes for poor style. Solution? Start the sentence with a gerund:
"Maintaining the value of a currency falls
within / is part of the remit of the
central bank.
„Spadat do kompetence“ is used much more in Czech than the literal
translation into English is, and the problem is with „competence“, which (in
native-speaker use) almost always conveys the idea of „ability“, not
„authority“, although it can mean „authority“. But the
word „competence“ tends to be avoided in this kind of context because of the
risk of ambiguity.
„Appertains within“ is very unusual in
native-speaker English, because „appertain“ is followed by „to“.
„Appertains“ is formal to the point of being over-formal, even in a
„formal academic“ context.
Here's an example of a very similar sentence structure in „formal“
(Council of Europe) style:
24. Ensuring respect of ethical principles and rules of conduct is part of
the remit of the SJC which decides when to initiate disciplinary proceedings.
(rm.coe.int)