Feature request: Import or continue claude.ai conversations in Claude Code

Problem

There is no way to bring a conversation from claude.ai (web/desktop) into Claude Code. The two products share the same underlying model and company, but their conversation histories are completely siloed.

A very common workflow is:

1. Brainstorm or scope out an idea with Claude on claude.ai (easier for long-form discussion, mobile, etc.).
2. Move to Claude Code to actually implement it.

Today the only way to carry context across is to ask claude.ai to summarize the discussion into a markdown blob and paste it into Claude Code. That works, but it feels like the wrong answer within the same Claude platform — especially when third-party MCP integrations (Slack, Notion, Gmail, Google Drive, etc.) can pull in external conversations, yet Claude's own conversation history cannot.

Current workaround

• Ask claude.ai to produce a markdown summary / brief
• Copy-paste it into Claude Code as initial context
• Lose nuance, intermediate reasoning, and attachments along the way

Proposed solutions (any of these would help)

1. First-party claude.ai MCP server — search and fetch past claude.ai conversations from inside Claude Code, the same way the Slack/Notion MCPs work.
2. claude --import <conversation-id> / \"Continue in Claude Code\" button — a direct handoff from a claude.ai conversation into a new Claude Code session with the transcript as context.
3. Structured export format — at minimum, make the claude.ai \"Export data\" output trivially consumable by Claude Code (e.g. claude --import-export ./export.zip).

Why this matters

It is genuinely strange that Claude Code can read my Slack DMs and Notion pages but cannot read the conversation I had with Claude itself thirty minutes ago. Closing this gap would make Claude feel like a single continuous assistant across surfaces instead of two disconnected products that happen to share a name.

Environment

• Claude Code CLI
• claude.ai web + desktop