If anyone is interested here is how I did it:

Enter developer mode. Go to settings ->technical->Filters. Create a new filter for model "invoice". Domain is [[u'partner_id.email', u'!=', False]]

It will appear under "favorites" 

Yes,

You can filter customer invoices by checking the field partner_id.email

You can set filters and save them as favorites in any tree view (list view) in the user interface, when you have activated the developer mode. And you can make them available even to all other users too.