How to automatically add the permission "edit" on a node to a user who is not the author?
Install Content Access and ACL, and then use Rules to add Person 1.2 as a person able to edit that content.

You may find this question helpful: Node access by role or user, what module(s) should I use?

The Content Access module gives you role permissions at the content type and (optionally) node level. By default, node level permissions are disabled but you can enable it on a type-by-type basis.
If you install ACL module, Content Access can give you per user permissions at the content type and node level.