It's a very useful feature to be able to share the URL (or some kind of identifier) to a PDF file stored in Zotero among the members of the same Group on Zotero.
You can just select the attachment in the web library and then copy the zotero.org URL from your browser address bar. Anyone in the group will be able to access it and then open the PDF from there.
You just can't share the files.zotero.net URL after viewing the file, since that's a temporary URL.
In a future version, we'll be making it possible to share a web library URL right from the desktop app.
Is it possible to share a link to the pdf of a paper from zotero such that anyone can open/download it?
With Mendeley, it was easy to store the pdfs in a dropbox folder, and share links to individual papers directly. But I'm intimidated by the folder structure of Zotero and haven't dared try to move it to Dropbox
If the person is not a member of your Zotero group(s) (which contains the PDF), you could make a copy of the PDF (finding it first via right-click Show File) to a cloud folder and then share the cloud service's file link.
Or if you use a cloud service to store a copy of your entire data folder for backup purposes, you could share PDF links from there instead.
In a "linked" PDF attachments setup (where linked PDFs [only] *can* be in a cloud folder) you can share a cloud PDF file link directly; for example from a single cloud folder that contains multiple PDFs (all your PDFs or just a subset). That can be important in a teaching environment, or similar cases where PDF distribution is common. But linked PDF files have significant other restrictions - they don't work in Groups, the web library, nor the mobile apps. https://www.zotero.org/support/attaching_files#linked_files
Note that in all those scenarios the PDF won't contain any annotations made in the Zotero reader, as those are stored in its database (but can be exported).
Upgrade Storage
You just can't share the files.zotero.net URL after viewing the file, since that's a temporary URL.
In a future version, we'll be making it possible to share a web library URL right from the desktop app.
With Mendeley, it was easy to store the pdfs in a dropbox folder, and share links to individual papers directly. But I'm intimidated by the folder structure of Zotero and haven't dared try to move it to Dropbox
https://www.zotero.org/support/kb/data_directory_in_cloud_storage_folder
If the person is not a member of your Zotero group(s) (which contains the PDF), you could make a copy of the PDF (finding it first via right-click Show File) to a cloud folder and then share the cloud service's file link.
Or if you use a cloud service to store a copy of your entire data folder for backup purposes, you could share PDF links from there instead.
In a "linked" PDF attachments setup (where linked PDFs [only] *can* be in a cloud folder) you can share a cloud PDF file link directly; for example from a single cloud folder that contains multiple PDFs (all your PDFs or just a subset). That can be important in a teaching environment, or similar cases where PDF distribution is common. But linked PDF files have significant other restrictions - they don't work in Groups, the web library, nor the mobile apps.
https://www.zotero.org/support/attaching_files#linked_files
Note that in all those scenarios the PDF won't contain any annotations made in the Zotero reader, as those are stored in its database (but can be exported).