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Mats, I have to rehabilitate you partially because I read now that in the
anglophone countries the problem friends use the denotation Moose for
that piece which was named as elk in the cited source (from Germany),
look e.g. to 'http://homepage.ntlworld.com/gpjnow/VC.htm'.

But here are fairy chess definitions for some others of your animals:

'Elephant': Queen+Nightrider, used also in some game variants, 
            e.g. 'Wolf Chess'
            (http://www.chessvariants.org/large.dir/wolf.html)

'Mammoth':  moves like a rook but only if it can capture
            (from A. M. Dickins: A guide to fairy chess.)

Alfred Pfeiffer