I am helping this new client find the problems with their website setup, one of the first things I noticed was their site was accessible at https://<domain> and https://www.<domain> their site was also appearing in google for both with and without www. Google will see both pages, with www and without www as two instances of the same page and may penalize for duplicate content. Setting the rel=canonical element (Canonical link) helps prevent this issue by telling google which copy is the right one.
This can be achieved through Worpress plugins like the WordPress Redirection plugin. But I also believe it’s wise to setup a 301 redirect for non www to www (or the other way around if you prefer) for a better user experience as well.
The 301 redirect to https://www<domain> can be done in the .htaccess file with the following rule;
# Redirect to www
RewriteCond %{HTTP_HOST} ^[^.]+\.[^.]+$
RewriteCond %{HTTPS}s ^on(s)|
RewriteRule ^ http%1://www.%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
Also of course, you want non http traffic redirected to https.. so no matter which way you hit the site you will end up with https://www<domain>
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