feat(09-05): implement ConvertTab + convertCertAction + render tests

- Add FileResponse interface to actions.ts
- Add convertCertAction(input, targetFormat): builds FormData with
  file/pemText/password + targetFormat, calls postForm convert endpoint
- Implement ConvertTab: native select for pem/der/p7b targetFormat,
  Konvertieren button with loading swap, error classification, empty state
- On success: calls downloadBase64(filename, content, mimeType)
- 3 new ConvertTab tests: format selector options, downloadBase64 invoked
  on success, text-destructive error on format rejection
- All 14 web cert-manager tests green

apps/web/src/app/(portal)/modules/cert-manager/actions.ts

@@ -116,6 +116,43 @@ export function downloadBase64(
   URL.revokeObjectURL(url);
 }
 
+// ---------------------------------------------------------------------------
+// FileResponse — mirrors CertManagerService.FileResponse
+// ---------------------------------------------------------------------------
+
+export interface FileResponse {
+  /** Suggested download filename, e.g. "converted.der" */
+  filename: string;
+  /** Base64-encoded file content */
+  content: string;
+  /** MIME type for the download */
+  mimeType: string;
+}
+
+// ---------------------------------------------------------------------------
+// convertCertAction — calls POST /modules/cert-manager/convert
+// ---------------------------------------------------------------------------
+
+/**
+ * Upload a certificate and convert it to the chosen target format.
+ * Returns a FileResponse — the caller should call downloadBase64(filename, content, mimeType).
+ *
+ * T-09-02: password is never placed in URL, logged, or echoed.
+ * T-09-04: credentials:'include' via postForm ensures JWT cookie is sent.
+ */
+export async function convertCertAction(
+  input: { file?: File | null; pemText?: string; password?: string },
+  targetFormat: string,
+): Promise<FileResponse> {
+  const { file, pemText, password } = input;
+  const form = new FormData();
+  if (file) form.append('file', file);
+  if (pemText) form.append('pemText', pemText);
+  if (password) form.append('password', password);
+  form.append('targetFormat', targetFormat);
+  return postForm('convert', form) as Promise<FileResponse>;
+}
+
 /**
  * POST a FormData payload to a cert-manager endpoint.
  * T-09-04: credentials:'include' ensures JWT cookie is sent for ModuleGuard.

apps/web/src/app/(portal)/modules/cert-manager/cert-manager.test.tsx

@@ -44,6 +44,7 @@ vi.mock('next-intl', () => ({
 import CertManagerPage from './page';
 import { InspectTab } from './components/InspectTab';
 import { SplitTab } from './components/SplitTab';
+import { ConvertTab } from './components/ConvertTab';
 import * as actions from './actions';
 
 afterEach(() => {
@@ -265,3 +266,74 @@ describe('SplitTab', () => {
     expect(errorEl.className).toContain('text-destructive');
   });
 });
+
+// ---------------------------------------------------------------------------
+// ConvertTab — unit tests
+// ---------------------------------------------------------------------------
+
+const MOCK_FILE_RESPONSE: actions.FileResponse = {
+  filename: 'converted.der',
+  content: btoa('fake der bytes'),
+  mimeType: 'application/x-x509-ca-cert',
+};
+
+describe('ConvertTab', () => {
+  it('renders format selector with pem, der, p7b options', () => {
+    render(<ConvertTab file={null} pemText="" password="" />);
+    const select = screen.getByRole('combobox');
+    const optionValues = Array.from(select.querySelectorAll('option')).map(
+      (o) => (o as HTMLOptionElement).value,
+    );
+    expect(optionValues).toContain('pem');
+    expect(optionValues).toContain('der');
+    expect(optionValues).toContain('p7b');
+  });
+
+  it('calls downloadBase64 after clicking Konvertieren when convertCertAction resolves', async () => {
+    vi.spyOn(actions, 'convertCertAction').mockResolvedValue(MOCK_FILE_RESPONSE);
+    const downloadSpy = vi.spyOn(actions, 'downloadBase64').mockImplementation(() => {});
+
+    const testFile = new File(['cert data'], 'cert.pem', {
+      type: 'application/x-pem-file',
+    });
+
+    render(<ConvertTab file={testFile} pemText="" password="" />);
+
+    // Click the Konvertieren button
+    fireEvent.click(screen.getByText('Konvertieren'));
+
+    // Wait for async action to resolve and downloadBase64 to be called
+    await waitFor(() => {
+      expect(downloadSpy).toHaveBeenCalledWith(
+        MOCK_FILE_RESPONSE.filename,
+        MOCK_FILE_RESPONSE.content,
+        MOCK_FILE_RESPONSE.mimeType,
+      );
+    });
+  });
+
+  it('shows text-destructive error when convertCertAction rejects with format error', async () => {
+    vi.spyOn(actions, 'convertCertAction').mockRejectedValue(
+      new Error('unknown format or invalid certificate'),
+    );
+
+    const testFile = new File(['garbage'], 'bad.bin', { type: 'application/octet-stream' });
+
+    render(<ConvertTab file={testFile} pemText="" password="" />);
+
+    fireEvent.click(screen.getByText('Konvertieren'));
+
+    await waitFor(() => {
+      expect(
+        screen.getByText(
+          'Unbekanntes Format. Die Datei konnte nicht als Zertifikat erkannt werden.',
+        ),
+      ).toBeInTheDocument();
+    });
+
+    const errorEl = screen.getByText(
+      'Unbekanntes Format. Die Datei konnte nicht als Zertifikat erkannt werden.',
+    );
+    expect(errorEl.className).toContain('text-destructive');
+  });
+});

apps/web/src/app/(portal)/modules/cert-manager/components/ConvertTab.tsx

@@ -1,6 +1,8 @@
 'use client';
 
+import { useState } from 'react';
 import { useTranslations } from 'next-intl';
+import { convertCertAction, downloadBase64 } from '../actions';
 
 interface ConvertTabProps {
   file: File | null;
@@ -8,15 +10,78 @@ interface ConvertTabProps {
   password: string;
 }
 
-export function ConvertTab({ file: _file, pemText: _pemText, password: _password }: ConvertTabProps) {
+type TargetFormat = 'pem' | 'der' | 'p7b';
+
+export function ConvertTab({ file, pemText, password }: ConvertTabProps) {
   const t = useTranslations('certManager');
+  const [loading, setLoading] = useState(false);
+  const [error, setError] = useState<string | null>(null);
+  const [targetFormat, setTargetFormat] = useState<TargetFormat>('pem');
+
+  async function handleConvert() {
+    setLoading(true);
+    setError(null);
+    try {
+      const response = await convertCertAction({ file, pemText, password }, targetFormat);
+      downloadBase64(response.filename, response.content, response.mimeType);
+    } catch (err) {
+      const msg = err instanceof Error ? err.message.toLowerCase() : '';
+      if (msg.includes('password') || msg.includes('passwort')) {
+        setError(t('error.wrongPassword'));
+      } else if (
+        msg.includes('format') ||
+        msg.includes('invalid') ||
+        msg.includes('unknown')
+      ) {
+        setError(t('error.unknownFormat'));
+      } else {
+        setError(t('error.generic'));
+      }
+    } finally {
+      setLoading(false);
+    }
+  }
+
+  const canConvert = Boolean(file || pemText);
 
   return (
     <div className="space-y-4">
+      {/* Target format selector */}
+      <div className="flex items-center gap-3">
+        <label htmlFor="targetFormat" className="text-sm font-medium text-foreground">
+          Ausgabeformat
+        </label>
+        <select
+          id="targetFormat"
+          value={targetFormat}
+          onChange={(e) => setTargetFormat(e.target.value as TargetFormat)}
+          className="rounded border border-border bg-background px-2 py-1 text-sm text-foreground focus:outline-none focus:ring-2 focus:ring-ring"
+        >
+          <option value="pem">PEM</option>
+          <option value="der">DER</option>
+          <option value="p7b">P7B</option>
+        </select>
+      </div>
+
+      {/* Primary action button */}
+      <button
+        onClick={handleConvert}
+        disabled={loading || !canConvert}
+        className="bg-primary text-primary-foreground px-4 py-2 rounded text-sm font-medium disabled:opacity-50 hover:opacity-90 transition-opacity"
+      >
+        {loading ? t('actions.processing') : t('actions.convert')}
+      </button>
+
+      {/* Error state */}
+      {error && <p className="text-sm text-destructive">{error}</p>}
+
+      {/* Empty state — shown when no error */}
+      {!error && (
         <div className="text-center py-8 space-y-1">
           <p className="text-sm font-medium text-foreground">{t('emptyState.convert')}</p>
           <p className="text-sm text-muted-foreground">{t('emptyState.convertBody')}</p>
         </div>
+      )}
     </div>
   );
 }