I get this request once in a while where users wants to checkout PDF document hosted in SharePoint from within Adobe Acrobat Reader or once check-out from SharePoint they want to check that document back in (or save the document) to SharePoint from Adobe Acrobat Reader.
Now if you are using SharePoint 2013 out of the box you may not get this feature. Fortunately there is simple configuration change that you would need to make to have this feature.
On all your SharePoint web front-end servers you would need to edit your DOCICON.xml file and update the PDF mapping to the following.
<Mapping Key=”pdf” Value=”icpdf.png” EditText=”Acrobat Reader” OpenControl=”AdobeAcrobat.OpenDocuments” OpenApp=”AcroRd32″/>
When changing this entry I was reading that it was recommended to perform IISRESET but that is only needed if you need this change to kick in right away. If you can wait then this change does not even require app pool recycle. In my case I had to wait roughly couple of hours (not 100% sure).
Nick Patel also have blogged about this in details if you are looking for additional information.
https://nikpatel.net/2012/09/09/improved-pdf-support-in-sharepoint-2013-delivers-better-user-experience/