How to change/disable password complexity test when changing password?

Ok, I will answer my question :)

I've found that pam_unix module performs password complexity check and it can be configured.

man pam_unix:

   minlen=n
       Set a minimum password length of n characters. The default value is
       6. The maximum for DES crypt-based passwords is 8 characters.

   obscure
       Enable some extra checks on password strength. These checks are
       based on the "obscure" checks in the original shadow package. The
       behavior is similar to the pam_cracklib module, but for
       non-dictionary-based checks.

Solution:
Alter the line in the pam_unix module in the /etc/pam.d/common-password file to:

password    [success=1 default=ignore]  pam_unix.so minlen=1 sha512

It allows you to set any password with minimal length of 1.

If it is a once off, using the passwd command as root you can set a simple password for a user by simply entering the desired value.

sudo su && passwd username

and then enter the password two times at the prompts.

Open the common-password config file for editing:

sudo -H gedit /etc/pam.d/common-password

Comment this line by adding the # character to the front as shown:

#password   [success=2 default=ignore]  pam_unix.so obscure use_authtok try_first_pass sha512

Also comment this line, otherwise password setting will ask you to pass a mix of upper/lower case letters:

#password   requisite           pam_passwdqc.so enforce=everyone max=18 min=disabled,8,8,1,1 retry=2 similar=deny

Now just add this line into the same file:

password    [success=1 default=ignore]  pam_unix.so minlen=1 sha512

this should do it...