301 redirect??

Can I take a page on one domain, redirect it to another domains page, and keep all of the backlinks, authority, etc from the original page.

Page A on Site 1 gets redirected to Page A on Site 2

the content and purpose of the page would be the same, the niche would be the same, in fact if it is possible i will completely copy the page. The page will disappear on Site 1 and reappear on Site 2.