[FEATURE] Reference Web Chat Conversations in Claude Code

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Context switching between Claude web interface and Claude Code CLI breaks workflow continuity and loses valuable context.
When working on complex technical problems, I often start discussions in the Claude web interface (especially when sharing screenshots, diagrams, or working on mobile/different devices) and then want to continue the same work in Claude Code CLI for hands-on development. Currently, there's no way to reference or import previous web chat conversations into the CLI environment.

Specific workflow pain points:

Start troubleshooting on mobile during commute, need to continue on laptop CLI at office
Share images/screenshots easily in web interface, but lose that visual context in CLI
Develop configurations and solutions in web chat, then manually copy/paste everything to CLI
Team members share chat URLs, but can't continue the technical work in their CLI environment
Complex multi-session projects lose context when switching between interfaces

Current workaround Manual copy/paste of conversation content, which loses formatting, images, and conversational context.

Proposed Solution

Add the ability to reference and import web chat conversations into Claude Code CLI sessions.

# Reference a specific web chat
claude --reference-chat https://claude.ai/chat/[chat-id]

# Import conversation context
claude --import-conversation [chat-url]

# Auto-sync with recent web conversations
claude --sync-context

Alternative Solutions

Manual copy/paste approach: Copy entire web chat conversations and paste them into CLI sessions. This is tedious, loses formatting, and doesn't preserve image context or conversation structure.

Priority

Medium - Would be very helpful

Feature Category

API and model interactions

Use Case Example

Morning (mobile): While commuting, I notice build failures. I start troubleshooting in Claude web interface, sharing screenshots of error logs and discussing potential solutions.
At office: I want to continue the work in Claude Code CLI to implement the fixes directly in my repository.
Current problem: I have to manually copy/paste the entire conversation, losing the screenshots and conversation flow.

Additional Context

_No response_