recover my authorization without Id

This is a trick that Adobe arranges for unsuspecting customers.

It did warn you, but not in nearly strong enough language.

Authorization without ID actually means authorization with an anonymous/implicit ID.

This implicit ID is much more restrictive than a real ID and can't be shared between computers or eReaders.

When a DRM book is downloaded (and the .acsm stub converted to a DRM .epub) the ebook is locked forever to the ID in use at the time.

There is no official way to transfer a book to a different ID.

Three things might work, but not at all sure ...

1) You can explain to the sellers and if they are feeling very kind they might let you download again.

But that is equivalent to saying to a real bookseller: "I dropped my book in the river, will you give me a new one free, please?",

so don't feel hard against them if they don't. 

Reserve your anger for Adobe who deserve it for providing this inept ADEPT DRM implementation.

2) You can try de-authorizing ADE on your PC again (using ctrl-shift-D to ADE; cmd-shift-D for a Mac);

restart ADE and see if you can now read the book.

But I am afraid that ADE will generate a new implicit ID, not regenerate the original one with which the book is associated.

3) If you have a complete system backup from before you registered with your proper ID you should be able to recover the book.

Then use ePubee or similar DRM stripper before you register back with a real id (technically against book ts&cs; but justifiable in the circumstances).