I would like to create a database for user accounts, which Moodle uses for it's own user accounts but other websites that I own, such as email accounts will use the same username and password as the user account on Moodle does. So if I change my password or create a user account on e.g. Moodle, then I will have the same user account and same password automatically added to my other sites, like Wordpress or my hosting plan's email system on 1and1.co.uk.
Is there any free way to do this?