Ideally you would Synchronise with your online account which became available in version X6 feature. The allows you to synchronise the references in your Endnote Desktop library with the references in your Endnote Online library.
Alternatively (but only one or two versions different), you must use a compressed Library to transfer it between computers. Instructions can be found on the EndNote website see link below
EndNote still recommend that you backup your library using the Compressed Library option on the File menu.
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