How to redirect forward from one subdomain to another subdomain with DNS?

redirect domain-name-system cname-record subdomain a-record

Not at all. Period.

DNS does not do browser redirects. What you do is have a website react to the old domains and issuing a HTTP Permanent Redirect (response 301).

A redirect like this CAN NOT BE DONE IN DNS.

Now, this may not be possible with Network Solutions hosting - but that is THEIR limitation, not a technical one.

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