It seems basic usage of Linux but I found out just today. If you want a user to be allowed to change group ownership of his files you must first use the command usermod (as root).
usermod -a -G group1 user1
After applying the command above (as root, or a user with enough privileges), the user user1 will be able to perform the following command chown user1.group1 file1 file2 file3 in order to change the files file1 file2 and file3 to another group.
usermod usually is inside /usr/sbin, if you don’t have this path inside your PATH environment variable, you must run the command /usr/sbin/usermod.</p>