I wanted to bring a design discussion from a Claude.ai web chat into a Claude Code session on a different project. Pasting the share link seemed like the obvious move, Claude Code can fetch plenty of pages, but a claude.ai share link only returns the static page shell, not the actual conversation underneath it. Printing the page to PDF didn't fare any better, same empty result.
The fix
Open the shared link in an actual browser tab first, not inside the Claude app itself, and let it fully render. The trick is that by the time a page is loaded that way, the conversation is already sitting in the rendered page, whether the original fetch could see it or not. A plain browser "Save Page As" (HTML) captures that rendered state, no extension required, and Claude Code can read the saved file directly.
A browser extension like Save HTML as Markdown gets you a cleaner result if you want to spend fewer tokens on it. A raw saved page carries all its markup along with it, class names, inline styles, embedded scripts and stylesheets, none of which is part of the actual conversation but all of which still counts against Claude Code's context window once read. The extension strips that down to just the real content, worth it for a heavy page, unnecessary for a short one.
Worth knowing before you go looking for something fancier
There's no built-in bridge between Claude's different surfaces today, a Claude.ai chat, a Claude in Chrome session, Claude Code, each one holds its own context with no shared memory between them. The same save-and-drop trick works regardless of which one you're pulling from: open it in a browser, save the rendered page, then hand that file to Claude Code directly. Small thing, but it saved me from re-explaining a decision I'd already worked through elsewhere.
It works the other way too
The same trick runs in reverse just as well. Open a Claude Code session's own web URL in a browser instead, let it render, and save the page the same way. Attach that saved file to a new Claude.ai web chat, and it reads straight in, no separate technique needed. The one difference: a Code session's URL isn't a public share link the way a claude.ai chat's is, so you'll need to already be logged into claude.ai in that browser for it to render the real content instead of a login screen.