History/Context: I have a site, 'www.oldexample.com' built in 1998, HTML 4.01 transitional on Apache, cpanel server. Until last fall our main keywords got us to top 10. After mobile changes and Panda etc, Dropped to page 2 or 3 for all but one very specific keyword. The old site, 'www.oldexample.com' has many good back links and history in google and all main directories. I am rebuilding a test site now which is on 'mycompany.myshopify.com' as it addresses all my google errors issues on oldsite. I have set up my 'www.newexample.com' to redirect to the shopify site which is called up under 'www.newexample.com'.The myshopify.com URL does not show up at all.
Question: If I were to do cpanel 301 redirect of whole 'oldexample.com' to 'newexample.com' would I still benefit from the many links and history of oldsite?