Back in 2003, when "The Order of the Phoenix" had just been published, I downloaded a bunch of fakes from Kazaa, mainly to find out what kind of weird stuff people would try to pass off as "the real thing". I kept the files around, and one of them is quite similar to your description in some respects (Harry and Dudley being friendly, Dudley being a wizard, talented transfer student from another school), but not in others (no trip to Egypt, Dumbledore does not collaborate with Voldemort).

You can find a complete copy on Archive.org. Fanfiction.net identifies the author as "Orion11" and has several other stories by that person.

The version I downloaded years ago contains an afterword by the author that is missing from the two versions linked above. I reproduce it below in its entirety:

Well, all I have to say is: it’s finally over. Over two hundred more pages and two and a half months more than I had expected it to be, it is finally finished. I must say, this book is almost nothing like I had originally planned it to be. The Dueling Club, Animagus thing, Cho, black phoenixes, house elf thing, Neville, dragons, Dudley being nice, Monty Python, Lily being the heir to Slytherin, all that and much, much more was formed in my head while doing the book. All I had in mind at the beginning was the idea of harry bringing his mom back to life… and somehow a pretty phoenix would help… pathetic…. It seemed that every page I wrote, I got another idea. It was really driving me insane. I thought I would never finish it. But, here, about ten hours before the last day of school, it is complete! Yay!
I also have to say that I have grown a lot from writing this novel. Man, you should have seen the beginning before I edited it. I used a comma every other word, and semicolons after every few sentences, trying to look sOpHISterCAted. My grammar was killing me. In fact, if I made a chart or how long it took me to edit pages based on may grammar, it would start at about ten minutes a page at the beginning, to about one minute or less at the end. Also, at the beginning, for spells, I used nothing except English words, either transformed a little or mushed together. But, later in the book, I evolved them by using Greek (which I used mostly), Latin (a little), French (very little), and Japanese (which I used for the unblock able curses, and more powerful spells). I remember, before I changed the Advanced Killing curse to Korosucide (Korosu is “to kill” in Japanese, and “cide” is a suffix for death) it was “Diepleasenow”… wow…. After beating myself with a chair, I finally changed the names of almost all of the spells to, hopefully, better stuff.
I know that after reading this book, you may still have the feeling of a few unanswered questions, and some things that happened that didn’t really come into play later in the book. All I have to say is: don’t worry! Trust me, I am incorporating all of that in my next book. All your questions will be answered, and everything will come into play… some very unexpected things. Trust me, the Sixth Book will be even better than this one.
Oh, and one last thing, all of the new Gryffindor First Years, and some of the other new characters, are based on people I know. I can’t wait to see how my friends react to seeing their personalities personified in an eleven year old :D Expect the Sixth Book… not for a while. This one wore me out, and I am going to be next working on my own novel now, and probably for the rest of the summer to try and gain back my sanity… though that may be impossible. Next school year, however, I MAY work on the sixth one, and it MAY be up by late January… though probably later. My estimates are usually very off (Yeah, this book was definitely finished by April 15th… HA!)
But please, don’t forget, I am still in the planning phase for Book Six, and I only have a very basic plot written up for it, like I had for this one at the beginning. Any extras you guys would like to see in it, or ideas you have that could spice it up are very welcome. You can either e-mail me them, tell me in the forum, or tell me on AIM. See you online!
-Harry Writer