diff --git a/frontend/src/pages/Register.jsx b/frontend/src/pages/Register.jsx
index 80bcbcd..4acb6a2 100644
--- a/frontend/src/pages/Register.jsx
+++ b/frontend/src/pages/Register.jsx
@@ -3,30 +3,7 @@ import { supabase } from '../supabaseClient';
 import { Link } from 'react-router-dom';
 import { motion as Motion } from 'motion/react';
 import { Mail, Lock, User, ArrowRight, AlertCircle, CheckCircle2, Eye, EyeOff } from 'lucide-react';
-
-/* eslint-disable react-refresh/only-export-components -- test-only helper exports */
-// Generous 5 min: a false "already exists" for a genuinely new user is worse
-// than missing a duplicate.
-export const EXISTING_ACCOUNT_AGE_MS = 300_000;
-
-export const DUPLICATE_ACCOUNT_MESSAGE =
-  "An account with this email already exists — log in or reset your password.";
-
-// Supabase returns identities: [] when the email is already registered (confirmed
-// account). For an unconfirmed duplicate, identities come back non-empty but the
-// account's created_at is old (Supabase re-signup doesn't reset it). A missing or
-// unparseable created_at, or missing identities, is treated as a fresh account.
-export function isExistingAccount(user, now = Date.now()) {
-  if (!user) return false;
-  if (user.identities?.length === 0) return true;
-  if (user.created_at) {
-    const createdAt = Date.parse(user.created_at);
-    if (!Number.isNaN(createdAt) && now - createdAt > EXISTING_ACCOUNT_AGE_MS) {
-      return true;
-    }
-  }
-  return false;
-}
+import { isExistingAccount, DUPLICATE_ACCOUNT_MESSAGE } from '../utils/registerHelpers';
 
 export default function Register() {
   const [email, setEmail] = useState('');
@@ -44,7 +21,7 @@ export default function Register() {
     const oauthError = localStorage.getItem('oauth_login_error');
     if (oauthError) {
       setError(oauthError);
-      setErrorKind(null);
+      setErrorKind(oauthError.includes('already exists') ? 'duplicate' : null);
       localStorage.removeItem('oauth_login_error');
     }
   }, []);
diff --git a/frontend/src/pages/__tests__/Register.test.jsx b/frontend/src/pages/__tests__/Register.test.jsx
index e2ebf26..a0225d2 100644
--- a/frontend/src/pages/__tests__/Register.test.jsx
+++ b/frontend/src/pages/__tests__/Register.test.jsx
@@ -4,7 +4,8 @@
 import { describe, it, expect, vi, beforeEach, afterEach } from 'vitest';
 import { render, screen, fireEvent, waitFor, cleanup, act } from '@testing-library/react';
 import { BrowserRouter } from 'react-router-dom';
-import Register, { isExistingAccount, EXISTING_ACCOUNT_AGE_MS } from '../Register';
+import Register from '../Register';
+import { isExistingAccount, EXISTING_ACCOUNT_AGE_MS } from '../../utils/registerHelpers';
 
 // Mock Supabase
 vi.mock('../../supabaseClient', () => ({
@@ -496,6 +497,14 @@ describe('Register', () => {
     expect(localStorage.getItem('oauth_login_error')).toBeNull();
   });
 
+  it('shows log-in link for OAuth existing-account error from localStorage', () => {
+    localStorage.setItem('oauth_login_error', 'An account with this Google account already exists. Please login instead.');
+
+    renderRegister();
+
+    expect(screen.getByRole('link', { name: /^log in$/i })).toBeInTheDocument();
+  });
+
   it('handles Google OAuth error', async () => {
     const { supabase } = await import('../../supabaseClient');
     supabase.auth.signInWithOAuth.mockResolvedValue({
diff --git a/frontend/src/utils/registerHelpers.js b/frontend/src/utils/registerHelpers.js
new file mode 100644
index 0000000..f88c041
--- /dev/null
+++ b/frontend/src/utils/registerHelpers.js
@@ -0,0 +1,24 @@
+// Pure helpers for Register: duplicate-account detection after supabase.auth.signUp.
+
+// Generous 5 min: a false "already exists" for a genuinely new user is worse
+// than missing a duplicate.
+export const EXISTING_ACCOUNT_AGE_MS = 300_000;
+
+export const DUPLICATE_ACCOUNT_MESSAGE =
+  "An account with this email already exists — log in or reset your password.";
+
+// Supabase returns identities: [] when the email is already registered (confirmed
+// account). For an unconfirmed duplicate, identities come back non-empty but the
+// account's created_at is old (Supabase re-signup doesn't reset it). A missing or
+// unparseable created_at, or missing identities, is treated as a fresh account.
+export function isExistingAccount(user, now = Date.now()) {
+  if (!user) return false;
+  if (user.identities?.length === 0) return true;
+  if (user.created_at) {
+    const createdAt = Date.parse(user.created_at);
+    if (!Number.isNaN(createdAt) && now - createdAt > EXISTING_ACCOUNT_AGE_MS) {
+      return true;
+    }
+  }
+  return false;
+}