It should be possible to open iCloud Pages documents in iWork Pages and simply save them in Pages format.
Convert Apple Pages iCloud document file to Pages document.
We have found one software suitable in our database for this conversion.
Apple macOS / Mac OS X software - convert pages-tef to pages on OS X
A word processor and layout tool marketed by Apple
Convert from pages-tef file format
|Yes, Pages for Mac supports pages file conversion as a target file type.||Yes||Yes||pages editor||Yes||No||No||No|
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.