In that case we recommend adding the new domain as an addon domain (not an alias) and then you can use .htaccess to redirect all the traffic from journalpulse.heliohost.us to synapsejournals.dedyn.io. I set the new domain as your main domain, and the heliohost.us subdomain as an addon. I also put an .htaccess file on the journalpulse.heliohost.us with these contents:
RewriteEngine on
RewriteCond %{HTTP_HOST} ^journalpulse.heliohost.us [NC,OR]
RewriteCond %{HTTP_HOST} ^www.journalpulse.heliohost.us [NC]
RewriteRule ^(.*)$ https://synapsejournals.dedyn.io/$1 [R=301,L,NC]
This should redirect everything to the new domain with a permanent redirect which means search engines and browsers should update their links. This .htaccess should preserve the path and filename so if someone goes to journalpulse.heliohost.us/path1/file2 it should send them to synapsejournals.dedyn.io/path1/file2, but if you're having any issues feel free to customize the .htaccess as you need. Eventually if you stop seeing any traffic to the heliohost.us subdomain in your web statistics let us know and we can remove the domain entirely to save server resources. Let us know if you need help with anything else.