Manager's annotations don't show up when traversing ForeignKey

Question

Suppose I have such classes:

class UserManager(Manager):
    def get_queryset(self):
        return super().get_queryset().annotate(
            full_name=Concat(
                F('first_name'), Value(' '), F('last_name'),
                output_field=CharField()
            )
        )


class User(Model):
    first_name = CharField(max_length=16)
    last_name = CharField(max_length=16)

    objects = UserManager()


class Profile(Model):
    user = ForeignKey(User, CASCADE, related_name='profiles')

And I want to include an annotated field in my query:

Profile.objects.filter(GreaterThan(F('user__full_name'), Value(24)))

But I got a FieldError: Cannot resolve keyword 'full_name' into field. Choices are: first_name, id, last_name, profiles

It's clear that I could repeat my annotation in a current query:

Profile.objects.filter(GreaterThan(Concat(F("user__first_name"), Value(" "), F("user__last_name"), output_field=CharField(),), Value(24)))

But as soon as my annotations will become more complex, my code become mess. Is there any workaround?