Here are some that might be them:
https://www.fanfiction.net/community/Harry-Potter-Characters-read-the-Harry-Potter-books/85285/
https://www.fanfiction.net/community/Time-to-Read-the-Harry-Potter-Books/91042/
https://www.fanfiction.net/community/Stories-About-Characters-That-Read-the-Harry-Potter-Books/87136/
:)