From Premium LI search features automate -> Public Profile, then connecting (saves InMails)
People like me pay for LI premium stuff because there are more search features and we narrow down the results further than regular LI searches. You can not "export" that list in regular LI but you can go through that list and click on "Public Profile" and then connect (or message, if they are 1st). I think you should automate that first process from a recruiter Lite or other premium search tools in LI. This will allows us to connect with more relevant people with your tool and save a ton on InMails.