The wp_password_change_notification function is responsible for this functionality inside WordPress that emails admins these user password change updates (as other posts have mentioned).

What I haven't seen here is that inside ./wp-includes/default-filters.php ~line 499 (at the time of this writing) you'll see this function being added to the after_password_reset action.

A quick fix is then to simply remove it from the action list:

remove_action( 'after_password_reset', 'wp_password_change_notification' );

You absolutely can rewrite/overwrite wp_password_change_notification, as it is one of the pluggable.php functions, but if you're looking to remove this functionality rather than update it, this might be a better option.

edit: this is to disable only the admin notifications when any other site user changes their password. I may have misread the question! Apologies =]

The wp_password_change_notification function is responsible for this functionality inside WordPress that emails admins these user password change updates (as other posts have mentioned).

What I haven't seen here is that inside ./wp-includes/default-filters.php ~line 499 (at the time of this writing) you'll see this function being added to the after_password_reset action.

A quick fix is then to simply remove it from the action list:

remove_action( 'after_password_reset', 'wp_password_change_notification' );

You absolutely can rewrite/overwrite wp_password_change_notification, as it is one of the pluggable.php functions, but if you're looking to remove this functionality rather than update it, this might be a better option.