Paths corruption after moving just uploaded files in CKEditor

To reproduce:
1. Upload a file using the "Upload file" button in CKEditor.
2. Move the image (Ctrl+X, Ctrl+V).
3. Open the image properties. You will see the corrupted image/link paths:
In FF 7, 11 the base path disappears (right: "/files/styles/...", after moving: "files/styles/...") both for the image and link.
In FF 12 the relative path is replaced with the absoulte (right: "/files/styles/...", after moving: "http://example.com/files/styles/...").
In Opera 11.62 (the lastest version for Win) the image path is OK but the link path disappears completely (is empty).

OS on the client side: WinXP SP3 (tested on the 2 different computers).

Moving the previously uploaded images (after saving the node) works fine.