diff --git a/docker/frontend/scripts/pwa-check.mjs b/docker/frontend/scripts/pwa-check.mjs
index f3068eb..5eca073 100644
--- a/docker/frontend/scripts/pwa-check.mjs
+++ b/docker/frontend/scripts/pwa-check.mjs
@@ -1,7 +1,7 @@
 // Install support is not visible in the source. It is the manifest the browser
 // reads, the worker it registers, and what that worker still holds once the network
 // is gone — so unlike the other checks here, which read a module and assert on it,
-// this one has to drive a real browser at a real build. Four assertions, one line
+// this one has to drive a real browser at a real build. Five assertions, one line
 // each, against a preview server:
 //
 //   npx vite build && npx vite preview --port 4183 &
@@ -25,7 +25,7 @@ const browser = await chromium.launch({
 });
 const context = await browser.newContext();
 
-// Every assertion prints, rather than throwing on the first one: which of the four
+// Every assertion prints, rather than throwing on the first one: which of the five
 // works and which does not is the whole answer.
 let failed = 0;
 const check = (ok, label) => {
@@ -78,9 +78,39 @@ try {
 }
 check(/RecipesCam/.test(brand ?? ''), `offline reload of /app paints the app's own header: ${brand}`);
 
+// (e) The offer is asked once. The browser's sheet is stubbed, because a check cannot
+// click the real one: waved away it is a refusal, and a refusal is stored, so the next
+// visit renders no dialog at all. The stub goes in an init script so it is there on
+// both loads.
+await context.setOffline(false);
+await page.addInitScript(() => {
+  window.__offerInstall = () => {
+    const event = new Event('beforeinstallprompt');
+    event.prompt = () => Promise.resolve();
+    event.userChoice = Promise.resolve({ outcome: 'dismissed' });
+    window.dispatchEvent(event);
+    window.dispatchEvent(new Event('rc:install-offer'));
+  };
+});
+const offer = async () => {
+  await page.evaluate(() => window.__offerInstall());
+  await page.waitForTimeout(150);
+  return page.locator('[data-key="install-yes"]').count();
+};
+await page.reload();
+const first = await offer();
+await page.locator('[data-key="install-yes"]').click();
+const stored = await page.evaluate(() => localStorage.getItem('rc.install.dismissed.v1'));
+await page.reload();
+const again = await offer();
+check(
+  first === 1 && stored === '1' && again === 0,
+  `install dialog shown ${first} time(s), refused (localStorage '${stored}'), shown again after reload: ${again}`,
+);
+
 await browser.close();
 if (failed) {
-  console.error(`pwa-check: ${failed} of 4 failed`);
+  console.error(`pwa-check: ${failed} of 5 failed`);
   process.exit(1);
 }
 console.log('pwa-check ok');
diff --git a/docker/frontend/src/pwa/install.ts b/docker/frontend/src/pwa/install.ts
index 92298bb..3bb9d77 100644
--- a/docker/frontend/src/pwa/install.ts
+++ b/docker/frontend/src/pwa/install.ts
@@ -2,8 +2,8 @@
 // whenever it likes, and the event has to be held until a click spends it — so this
 // is a module-level slot plus a subscriber list, and no store, hook or context.
 //
-// The one piece of state the visitor owns is the refusal: remember it, and the offer
-// never comes back. A dismissal is an answer, not a snooze.
+// The state the visitor owns is the answer: a refusal, or an install. Remember either
+// one, and the offer never comes back. A no is an answer, not a snooze.
 
 type InstallEvent = Event & {
   prompt: () => Promise<void>;
@@ -11,6 +11,9 @@ type InstallEvent = Event & {
 };
 
 const DISMISSED = 'rc.install.dismissed.v1';
+// The other answer: installed, and never asked again — including from a plain browser
+// tab, which has no `standalone` to tell it so.
+const INSTALLED = 'rc.install.installed.v1';
 
 // The window event a control elsewhere in the app (the Library's own button, say)
 // fires to pull the offer forward instead of waiting out the delay.
@@ -33,11 +36,15 @@ export function subscribe(listener: () => void): () => void {
 }
 
 export function canInstall(): boolean {
-  return deferred !== null && !dismissed();
+  return deferred !== null && !dismissed() && !isInstalled();
 }
 
 // Spends the browser's prompt and reports the answer. Null means there was nothing
 // to spend: the event never arrived, or this is a second call.
+//
+// Either answer is remembered, because either answer is the visitor's: yes is the app
+// being installed, and the browser's own sheet being waved away is a no — the event is
+// spent now, and it never fires again for this install.
 export async function promptInstall(): Promise<'accepted' | 'dismissed' | null> {
   const event = deferred;
   if (!event) return null;
@@ -47,6 +54,8 @@ export async function promptInstall(): Promise<'accepted' | 'dismissed' | null>
   notify();
   await event.prompt();
   const { outcome } = await event.userChoice;
+  if (outcome === 'accepted') markInstalled();
+  else dismissInstall();
   return outcome;
 }
 
@@ -76,6 +85,18 @@ export function dismissInstall(): void {
   notify();
 }
 
+// True in the installed window itself, and also in any browser tab that watched the
+// install happen — that tab keeps running the site, and must not ask for the app it
+// just installed.
+export function isInstalled(): boolean {
+  return isStandalone() || localStorage.getItem(INSTALLED) === '1';
+}
+
+export function markInstalled(): void {
+  localStorage.setItem(INSTALLED, '1');
+  notify();
+}
+
 // Asks for the offer now.
 export function offerInstall(): void {
   window.dispatchEvent(new Event(OFFER_EVENT));
@@ -93,5 +114,5 @@ window.addEventListener('beforeinstallprompt', (event) => {
 // and is the only signal that the offer is done.
 window.addEventListener('appinstalled', () => {
   deferred = null;
-  notify();
+  markInstalled();
 });
diff --git a/docker/frontend/src/ui/InstallPrompt.tsx b/docker/frontend/src/ui/InstallPrompt.tsx
index 7d78f8b..2339a4e 100644
--- a/docker/frontend/src/ui/InstallPrompt.tsx
+++ b/docker/frontend/src/ui/InstallPrompt.tsx
@@ -5,8 +5,8 @@ import {
   canInstall,
   dismissInstall,
   dismissed,
+  isInstalled,
   isIosSafari,
-  isStandalone,
   promptInstall,
   subscribe,
 } from '../pwa/install';
@@ -30,7 +30,7 @@ export function InstallPrompt() {
   useEffect(() => {
     // An installed app has nothing to offer, and a refusal is final — the visitor
     // said no to this dialog, not to this session.
-    if (isStandalone() || dismissed()) return;
+    if (isInstalled() || dismissed()) return;
 
     const manual = isIosSafari();
     let waited = false;
@@ -86,8 +86,8 @@ export function InstallPrompt() {
             type="button"
             className="btn primary"
             data-key="install-yes"
-            // Not a dismissal: taking the offer and waving the browser's own sheet
-            // away are different answers, and the app's own button can still ask.
+            // `promptInstall` records the browser's answer itself: accepted means the
+            // app is installed, waved away means the offer was spent and refused.
             onClick={() => {
               void promptInstall();
               setFace(null);