[FEATURE] Projects: threads running on a local folder (Remote Control) can't read or write project memory

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

In the Claude Code Projects beta, a project has a shared memory that the project's coordinator reads and writes with a memory tool. A thread that runs on a local folder on my PC (over Remote Control) can't reach that memory. The session has no memory tool, no memory server among its connectors, and no shared project folder. When the coordinator asked the local thread to read project memory, the thread couldn't find any way to do it.

The local thread only sees Claude Code's per-folder auto-memory on that machine (~/.claude/projects/<folder>/memory/), which the rest of the project can't see. So one project ends up with two memories that don't know about each other, and what a thread knows depends on where it runs.

Proposed Solution

Give Project threads that run on a local folder the same access to project memory that the coordinator has, so every thread in a project reads and writes one memory wherever it runs.

Alternative Solutions

Copying local memory files into the project by hand works once, but the two drift apart as soon as either side learns something new.

Related but different: #90973 (unify Claude Code memory with claude.ai memory) and #97201 (other rough edges of local-folder Project threads).

Priority

Medium - Would be very helpful

Feature Category

Other

Use Case Example

I'm a solo game developer. I've worked with Claude Code both locally on my Windows PC and in cloud sessions, so useful memories are spread across both. I'd like to move everything into one Project and consolidate those memories there, but some work (like running the game on my PC) has to happen in local threads. Today those threads would lose everything that's been consolidated.

Additional Context

Windows 11, Claude desktop app 2.7032.0, Claude Code 2.1.281, Projects beta. I checked from inside a local thread: its connectors were claude-code-remote, hearthbot, Claude Docs, Slack, visualize and scheduled-tasks, with no memory server.