Feature Request: Cross-device session sync between desktop and mobile

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

Claude Code sessions started on Mac cannot be continued on iPhone or mobile devices. When switching devices mid-project, all context is lost and must be re-entered from scratch, significantly reducing productivity.

Proposed Solution

Allow Claude Code sessions to be synced via Anthropic account, so that a session started on Mac can be resumed on iPhone (via browser or app). Similar to how OpenAI Codex handles cross-device continuity.

Alternative Solutions

Currently copying and pasting conversation history manually between sessions, but this is cumbersome and loses context.

Priority

Medium - Would be very helpful

Feature Category

Configuration and settings

Use Case Example

1. I start a Claude Code session on Mac to review a GitHub repository (law-office-automation).
2. I want to check the results or continue the session from my iPhone while away from my desk.
3. Currently, all context is lost and I must start over on mobile.
4. With cross-device sync, I could seamlessly continue work from any device.

Additional Context

OpenAI Codex supports cross-device session continuity between desktop and mobile. Claude Code currently has no equivalent feature.