Converting image to Jpeg2000 does not work

What am I doing wrong?

Nothing. The command you typed in is correct. The problem is that *.jp2 (JPEG 2000) support isn't built into the repository version of Imagemagick. When converting to an unsupported format the resulting destination file will be the same format as the source file.

You can verify this by looking at the fourth lines of the convert -version output:

$ convert -version

Output:

Version: ImageMagick 6.8.9-9 Q16 x86_64 2016-11-29 http://www.imagemagick.org
Copyright: Copyright (C) 1999-2014 ImageMagick Studio LLC
Features: DPC Modules OpenMP
Delegates: bzlib cairo djvu fftw fontconfig freetype jbig jng jpeg lcms lqr ltdl lzma openexr pangocairo png rsvg tiff wmf x xml zlib

Notice that jp2 isn't included.

This is a reported bug (imagemagick: missing JPEG-2000 support):

The bug report describes the problem and indicates it has been fixed in the latest release (Version 6.9.1.2-1) which hasn't reached the repository yet.

Another test for jp2 support is:

$ identify -list format | egrep -i jp2

There is a use at your own risk PPA at:
https://launchpad.net/~isage-dna/+archive/ubuntu/imagick

Update:

As provided by SamWilson in the commands a supported PPA which I tested is located at: https://launchpad.net/~lyrasis/+archive/ubuntu/imagemagick-jp2

sudo add-apt-repository ppa:lyrasis/imagemagick-jp2
sudo apt-get update