DNS question (CNAME)

I am trying to troubleshoot a problem for a friend, here is the run down:

He has 2 domains, we'll call them longurl.com and shorturl.com.
He wants it so when someone types in www.longurl.com it redirects to www.shorturl.com.

All he needs to do this is a DNS change, right?

This is how the nslookup is right now. I left out the MX, SOA and NS:
----------------------------

(longurl.com DNS info)
longurl.com CNAME www.shorturl.com
www CNAME www.shorturl.com

(shorturl.com DNS info)
shorturl.com A [ip address of site]
www A [ip address of site]

--------------------------------

This site has a static ip.
The only thing that I would have done, was instead of setting the CNAME to www.shorturl.com, I would just have set it to shorturl.com, but that shouldn't matter.

Any help would be appreciated and thank you in advance!

 

 

 

 

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