DEVELOPERS NOTE!
Yes, working with CWYW off and moving from computer to computer which is synced with the same online library is problematic and they haven’t yet fixed it. The record numbers are not maintained during the sync process. I find it very frustrating. I have worked out a couple of potential workarounds. Endnote (Edit>preferences>temporary citations on a PC) can be set to use one of three other fields,rather than the record number in your temporary citations. Accession number (but not all my references have an Accession number), page numbers (some electronic resources might not have page numbers though) or label. When you sync, that label field will be in both libraries and won’t be dependent on the library’s record number which is not permanent in synced libraries.
I prefer the label field, but that takes some work to generate and so it is a bit tedious. I copy my record numbers and entered a prefix and a suffix (depending on their source) to the label field. Since the matching program to the label is not “is” but “contains” you need to include the prefix and suffix to make it an exact match for the CWYW temporary citation.
So an example of the label is LMW4778XX, for example for a record that has a record number of 4778. I always do this from the same computer’s library. Regularly, I sort on label, select and show only those without a label, and then do the tools, Change/Move/Copy fields, and Copy the Record Number (you can only copy this field, you can’t move it) to Label (replacing what may be there before, but if those contents are important, you can first move them to another field using the same tool). Then repeat and put the prefix (LMW no space option in my example) and then repeat and put the suffix (XX in my example, no space). And you have created a unique record number. Now make sure your Endnote (Edit>preferences>temporary citations on a PC) are set to use the label rather than the record number in your temporary citations. – When you sync, that label field will be in both libraries and won’t be dependent on the specific library’s record number. You have to make this preferences change in Endnote on each of the computers.