Lifetime of lambda without capture [duplicate]

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• Lifetime of lambda objects in relation to function pointer conversion 1 answer

void set_callback(void (*fptr)());

void f() {
    auto callback = []() { std::cout << "callback" << std::endl; };
    set_callback(static_cast<void()>(callback));
}

set_callback is a library function that takes a function pointer void(*)() as argument. It will set a global state such that the function pointer is called after f has exited (possibly on another thread).

But callback is defined as a capture-less lambda in the scope of f, and converted to a function pointer when passed to set_callback. So its lifetime ends when f exits.

It the program still correct in this case? (Because the lifetime of the callback function itself is global).

If not, is it correct if callback is instead defined as static inside the function?