How to fix the Apple Mail search problem in MacOS X 10.7 Lion

After my update from MacOS X 10.6 Snow Leopard to 10.7 Lion the search function in Apple Mail stopped working.
There were no or too little search results, when I typed something in the search field.
It looked like my mailboxes couldn't be indexed by spotlight anymore.

And here is the simple solution:

1. Mark your mailbox in the list of mailboxes on the left in your apple mail window by clicking on its name once.
2. From the menu select "Mailbox" => "Rebuild".
3. After the rebuild you should get the right search results again.
4. Proceed with Step 1-2 for all your mailboxes (also for every top-level folder that is stored under "local" in your list of mailboxes).