This should work nicely if you know the old and the new Viewports.
var oldView; // Viewport to Copy from
var newView; // Viewport to Copy to
// Get old objects
var doc = Rhino.RhinoDoc.ActiveDoc;
var enumerSettings = new ObjectEnumeratorSettings()
{
ViewportFilter = oldView;
};
RhinoObject[] oldItems = doc.Objects.Find(enumerSettings);
// Add new objects
var attribs = new ObjectAttributes()
{
Space = ActiveSpace.PageSpace,
ViewportId = newView.Id
};
foreach(RhinoObject obj in oldItems)
{
var geom = obj.Geometry.Duplicate();
doc.Objects.Add(geom, attribs);
}