Welcome to the Q&A Forum

Hi All, I have been facing the same problem but still i have been confused so please see my thoughts below. We should be clear on @Melissa's question. 1 - He wants to know should we do the link-building on redirected domain or not. 2 - If we will do the link-building on redirected domain then what URL Google will follow and display in SERP. As he said this new website "stephenshefrinphotography.com" redirected to his old domain "shef1.com" , that means  new website domain is virtual and old one is real. If we will create the backlinks for new website in order to get good ranking and traffic that will work or not ? If it will work then what URL will come in search page stephenshefrinphotography.com or shef1.com. I am looking forward to hear from you soon. Thanks a lot in advance..

Wow, this is really great advice!  I'll get to work on your suggestions ASAP!

Not sure what you meant by " wont be wasting any content," A 301 redirect will only redirect incomming links to the new page, the content value of the old page or any inherent authority it had will not be passed. It will no lnger exist, only the incomming links will exist and can be redirected