Email account is generating spam with link inbedded in it

You can do a little detective work yourself.  Go into your online email account .... make sure you are in Classic (not Enhanced) webmail.  First look under SENT mail.  See if the spam was sent from your account.  If not, the spammers just copied her email address as their return address..  Then click on the blue SETTINGS button.  Open the one that says "Blocked..." .  See if you have any email addresses or domains in the boxes.  If you did not put them there yourself, the spammers did.  Remove them and click SAVE ( submit?) on that page.  Open the other Settings and make sure nothing is there that you did not select. 

Spammers don't usually hack your account by using your password, but it does happen.  Make a new password that is longer and more scrambled.

I called Cox support and a Tier 2 technician called the IP that was sending out the spam (using my email as the return address).  That fixed the problem for a while.

Did your wife get any notices titled "Mailer-Daemon, Undeliverable Mail, etc"?   Those are the spam emails that got caught in the different spam filters and bounced back.

@jeffr

From what you've described it does sound like here username/password have been compromised.  I'd suggest using a known safe computer to change her password to a new password which she has not used anywhere before as well as going a virus scan on all devices she uses to check for possible key logger infections.