ChatGPT’s memory lives in OpenAI; Claude’s lives on Anthropic’s servers. There is no shared store between them, so a fact you taught ChatGPT is invisible to Claude and vice versa.
In 2026 Claude added a one-time markdown import that can ingest a memory export from ChatGPT or Gemini. That helps when you move once, but it is a snapshot, not continuous sync — new memories created afterwards stay siloed again.
For memory that stays in sync across both, keep it in an independent layer. Alma stores your memory once and serves it to any MCP-compatible client, so the same context is available whether you are in Claude Desktop, Cursor or Alma’s own chat.