When I AirDrop a PDF from my iPhone to my iPad the document icon vanishes.
I create the PDF on my iPhone by first going to Reader View, then I tap the Share button and scroll to Create PDF. When the PDF is created, I tap the Share button again and tap Copy to Adobe Acrobat.
In Adobe Acrobat with the PDF open, I tap the Share button and go to Share File then I choose a format and share the PDF to my iPad via AirDrop. On my iPad when the pop up message appears, I tap to open with Adobe Acrobat. The document icon is now gone, but I can still read my PDF.