On RootWeb of both site collections I have created same User field (owner). I mean same user field becuase I used same ID (GUID), name and everything. Then I add the field to a content Type and add the content type to all Document libraries for both site collections. But still when I copy a document from a document library in a Site collection to another Document library within another site collection the value of owner field disappears. thanks for all advice.
if you do it programmatically you could refer to the hidden list located at _catalog/users/detail.aspx and try to find the User by it's name there and set it to the right id for the other site collection