RESOLUTION
To transfer a domain from one client to another the following Plesk command line utility is used:"%plesk_bin%\domain.exe" -u <domain name> -clogin <client login name> <domain name> - is the transferred domain name
<client login name> - is the login name of the client, receiving the domain.
Note: Starting from Plesk 7.6.1 such change can be done through Control Panel directly.