[FEATURE] Bi-directional context sync between Desktop and Terminal sessions

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

Problem

When teleporting from Desktop Claude Code to Terminal/CLI and doing work there,
there's no way to sync that context/work back to the Desktop session.

Proposed Solution

Proposed Solution

Add an option to send the Terminal/CLI session context back to the originating
Desktop app session, maintaining continuity of work across interfaces.

Alternative Solutions

No real alternatives found for this particular case

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

Use Case

1. Start planning/discussion in Desktop app
2. Teleport to Terminal for implementation (e.g., building a complete application)
3. Want to teleport back WITH all the work/context to Desktop for review/next steps

Additional Context

Current Behavior

• Desktop → Terminal teleport works
• But no way to bring Terminal work back to Desktop
• Context is lost when switching back