If you delete your account, the game will not magically unregister and they won't be able to use it either.
All you can do is give them your account but the problem is that I think you can't simply change your email address on the Origin Account anymore.
Best is to contact customer support and ask them how to proceed.
They can be found here: https://help.ea.com/contact-us
Choose a category, a game and a platform for the contact options to show up.
If live chat is gray, change your country to US and make sure you're on US Business hours. It might also gray because they're very busy. Try later.
See this post if you have trouble with the site: http://sims3.crinrict.com/en/2012/10/how-to-contact-ea.html
That would be helpful if it didn't take 30 minutes+ to wait for a chat session to open up (who has that kind of time to wait???). I also found Sims 3 to be absolutely terrible - I hated it. I want to delete my account completely, and am flabbergasted it is this difficult. I have to say I am very disappointed, and I can't see myself giving the sims another try ever again.
