We assign the project to the specific Role, not to the LeadLink, as the Lead Link is acting in the Role of the absent person, and not as the Lead Link.
(Generally, Projects are assigned to Roles not "partners".)
Acceptance is implied, or given by the LeadLink.
If the proper Role holder, looking at the Tactical Outputs, has a tension with the project that was assigned to them, well, that's a tension.
Does this help?