SharePoint 2013 has this quirk going for quite some time where clicking on a PDF file opens it in the browser no matter what you configure in the list settings or client application. One of our customers migrated to SharePoint 2013 and suddenly they lost this functionality. Together with my colleague Elio Struyf we proposed a small customization that would add the “Open in client” option to the fly out menu for PDF documents.
The customization itself is devised as a SharePoint Sandboxed Solution that can be installed and activated per Site Collection on either an on-premises environment or Office 365.
The functionality can be enabled or disabled via the corresponding Site Collection Feature.
The customisation can be found on GitHub: Ventigrate/SharePoint_PDFOpenInClient