Drag and Drop.   Yes, it retains the PDF icon.

The settings for files behavior when importing and downloading documents from LF using Drag and Drop is handled by the Options feature under the Tools Menu on the Ribbon. The Settings can be found under the Download or New Document settings

If you right click on the PDF file in LF, and choose edit Electronic File in LF, see if it is still a Fillable PDF? This would tell you whether your issue is on import or download.

We are using Web Access.  When I right click on the document I don't have an option to edit Electronic File. 

Sorry, Old School, thinking Client, not WebAccess. When you click on the file and choose Download in the top right just under the display options, you will get a Popup box to Download the file, the Default is set to Image, click on the word Image and a Drop down will appear, choose Electronic File.

I don't have an "Electronic File" option.  The only options available are Image, Text and Briefcase.

I figured it out.  When I import the document I have to uncheck "Generate Pages".  This leaves the PDF as an electronic document and now when I select "Download" I have the Electronic Document option.

Seems a little clunky though.  If I click on the name it opens the PDF in the document viewer but since it is an electronic document it only shows the text version.  I would expect that if you don't generate pages it should open a PDF the same way it opens all electronic documents, in the native client.

When I choose this option a new tab opens up but nothing is ever displayed in that tab.  Doesn't matter whether I choose View or Edit they both end in the same result, a new browser tab with nothing displayed in it.  The URL looks like it is for the PDF document but nothing is displayed.  I tried it in IE and Chrome and they both show the same behavior.

Do you have Acrobat Reader installed on the PC? I'd also try Firefox as they have a nice feature under their Options>Applications Tab that allows you to configure how Firefox will open a file.