docs: add ChatGPT and Claude memory sync examples

apps/docs/personal-brain/use-cases/browser-extension.mdx

@@ -1,7 +1,7 @@
 ---
-title: "Supermemory Chrome Extension: Save Webpages, Import Bookmarks, and Sync ChatGPT Memories"
+title: "Sync ChatGPT and Claude Memories with the Supermemory Chrome Extension"
 sidebarTitle: "Browser extension"
-description: "Learn how to use the Supermemory Chrome extension to save webpages, import Chrome bookmarks, and sync ChatGPT memories into your Personal Brain."
+description: "Learn how to sync ChatGPT and Claude memories with Supermemory, save webpages, and import Chrome bookmarks into your Personal Brain."
 icon: "globe"
 ---
 
@@ -9,7 +9,7 @@ Save what you read on the web without leaving the tab.
 
 ## How the Supermemory Chrome extension works
 
-The Supermemory Chrome Extension saves webpages, imports bookmarks, and syncs ChatGPT memories into your Personal Brain.
+The Supermemory Chrome Extension saves webpages, imports bookmarks, and syncs memories from ChatGPT and Claude into your Personal Brain.
 
 ## Before you start
 
@@ -40,13 +40,33 @@ The Supermemory Chrome Extension saves webpages, imports bookmarks, and syncs Ch
 
 ## How the extension talks to Supermemory
 
-The extension talks to Supermemory from Chrome. It saves the current page, imports bookmarks in bulk, or syncs ChatGPT memories into your active Space.
+The extension talks to Supermemory from Chrome. It saves the current page, imports bookmarks in bulk, or syncs memories from ChatGPT and Claude into your active Space.
 
 ## What the browser extension saves, imports, and syncs
 
 - Save: the current webpage and, optionally, a selection or note
 - Import: existing Chrome bookmarks
-- Sync: ChatGPT memories from a signed in ChatGPT session
+- Sync: memories created in signed in ChatGPT and Claude sessions
+
+## How to sync ChatGPT memories with Supermemory
+
+Once the browser extension is connected, ask ChatGPT to remember a preference, decision, or piece of project context. ChatGPT saves it through Supermemory so the memory can be recalled later from your Personal Brain and connected tools.
+
+<Frame>
+  <img src="/images/personal-brain/chatgpt-memory-sync.jpg" alt="ChatGPT confirming that a project preference was added to Supermemory" />
+</Frame>
+
+In this example, ChatGPT saves the project's update cadence and decision log as a memory. The **Memory updated** confirmation shows that the context is available for future conversations.
+
+## How to sync Claude memories with Supermemory
+
+In Claude, ask it to remember context that should carry into future work. Claude uses the connected Supermemory tools to save that context to the same Personal Brain used by ChatGPT.
+
+<Frame>
+  <img src="/images/personal-brain/claude-memory-sync.jpg" alt="Claude confirming that a research preference was saved with Supermemory tools" />
+</Frame>
+
+Here, Claude saves a research preference for the same project. Memories added from ChatGPT and Claude share one memory layer, so either assistant can work with the context available through Supermemory.
 
 ## Limitations of the browser extension
 
@@ -58,7 +78,7 @@ The extension talks to Supermemory from Chrome. It saves the current page, impor
 
 - **A saved page did not appear.** Check the active organization, active Space in the extension, and that the memory finished processing.
 - **Sign in loops.** Sign in to Supermemory at [app.supermemory.ai](https://app.supermemory.ai) first, then reopen the extension.
-- **ChatGPT sync didn't run.** Confirm you're signed in to ChatGPT in the same Chrome profile and the connection status is active.
+- **ChatGPT or Claude sync didn't run.** Confirm you're signed in to the assistant in the same Chrome profile and that the Supermemory connection is active.
 
 ## Related
 
@@ -70,4 +90,4 @@ The extension talks to Supermemory from Chrome. It saves the current page, impor
   <Card title="Spaces" icon="layers" href="/personal-brain/concepts/spaces">
     Keep different parts of your memory organized and separate.
   </Card>
-</CardGroup>
+</CardGroup>