What's the best approach of redirecting an old domain AS WELL all the internal pages from the old domain to the new domain?
Both are from shopify. Will the host provider need to be involved in this project? What plugin do you recommend?
Or is it simply a map to map process and we redirect it based on a plugin used? Thankfully, both sites do not have any traffic. But in long term, we want to ensure that there's only one true site, and that the other (which is indexed in Google), is redirected accordingly.
Point both domains to Shopify. In the domain settings, you can set a primary domain where all domains there redirect to the primary domain. This will result in all versions of pages on non-primary domains being redirected to their primary versions.
Internal linking should be updated for SEO to avoid internal 301s. It all depends on how the link is done. Shopify itself will not use the domain in links for things like navigation, but if you have absolute links in blog posts, theme settings, or even hard-coded into your theme, then you've got to manually hunt down each one and update.