It is possible to share documents and libraries, which can be very useful if you are collaborating with colleagues for example.  

Since sharing relies on the sync services, you must first set up your EndNote account and fully sync your library before you can share. If you've already done this, then just go to File > Share and enter the email addresses of the people you want to collaborate with (on EndNote X7 you can share your library with 14 other people compared to EndNote X8, which allows sharing with a 100 others). If you haven’t, start by clicking the Sync icon on the toolbar. You will be prompted to enter your account credentials or create a new account, if you haven’t done so already. Once your account is created and your library is fully synced, you can begin sharing.

Sync times can vary depending on the size of your library. Be sure to check the Sync Status, located in the My Library panel, to make sure your library is fully synced before sharing

For more details of how to sync your library, please see video below