import sys
from functools import wraps

def create_module_properties():
    properties = {}
    patched_modules = set()

    def patch_module(module):
        if module in patched_modules:
            return

        def base_getattr(name):
            raise AttributeError(f"module '{module.__name__}' has no attribute '{name}'")

        old_getattr = getattr(module, '__getattr__', base_getattr)

        def new_getattr(name):
            if name in properties:
                return properties[name]()
            else:
                return old_getattr(name)

        module.__getattr__ = new_getattr
        patched_modules.add(module)

    class ModuleProperties:
        @staticmethod
        def getter(func):
            @wraps(func)
            def wrapper():
                return func()

            name = func.__name__
            if name.startswith('_'):
                properties[name[1:]] = wrapper
            else:
                raise ValueError("Property function names must start with an underscore")

            module = sys.modules[func.__module__]
            patch_module(module)

            return wrapper

    return ModuleProperties()