No need! Maybe I didn't explain my idea well.
The idea was to put the BBCode of the quote in the transfer area
You wuold indeed need the session code to link directly to the quote-page, but not to copy the quote to the clipboard. Maybe TryNinja can take inspiration from the BPIP Extension:
Allow quoting posts from locked threads into clipboard. (on)
Then use paste this in your post.
This would be useful, in case the person is creating a post in another area of the forum and wants to fetch several quotes from other posts, without having to open the pages of these posts to generate the quote.
There's a flaw though: if the post has been edited, you're quoting the unedited version and that might mean you're quoting something that no longer exists.