Redirect after login

When users log into the system using a login form at “staff.example.com” (when WP is installed in “example.com”), I want to redirect them back to “staff.example.com”…

I’ve tried defining the hidden field ‘redirect_to’, but that doesn’t work.

I understand I need to modify wp_safe_redirect, namely the “allowed_hosts” part.

How would I modify that filter to include my custom subdomain?